Imaginäre biquadratische Zahlkörper mit Exponent 1,3,5.
Der wissenschaftliche Inhalt steht in der Arbeit:
J. Klüners, T. Komatsu, Imaginary multiquadratic number fields of exponent 3 and 5
Exponent 1
Die folgende Tabelle enthält alle imaginären biquadratischen Zahlkörper der Familie 2a mit Exponent 1. Die Ergebnisse sind ohne Verwendung einer Vermutung bewiesen.
Diskriminante | Faktorisierung | Erzeuger | Klassengruppe |
144 | 2^4 * 3^2 | -3, -4 | C1 |
256 | 2^8 | -4, -8 | C1 |
441 | 3^2 * 7^2 | -3, -7 | C1 |
576 | 2^6 * 3^2 | -3, -8 | C1 |
784 | 2^4 * 7^2 | -4, -7 | C1 |
1089 | 3^2 * 11^2 | -3, -11 | C1 |
1936 | 2^4 * 11^2 | -4, -11 | C1 |
3136 | 2^6 * 7^2 | -7, -8 | C1 |
3249 | 3^2 * 19^2 | -3, -19 | C1 |
5776 | 2^4 * 19^2 | -4, -19 | C1 |
5929 | 7^2 * 11^2 | -7, -11 | C1 |
7744 | 2^6 * 11^2 | -8, -11 | C1 |
16641 | 3^2 * 43^2 | -3, -43 | C1 |
17689 | 7^2 * 19^2 | -7, -19 | C1 |
23104 | 2^6 * 19^2 | -8, -19 | C1 |
29584 | 2^4 * 43^2 | -4, -43 | C1 |
40401 | 3^2 * 67^2 | -3, -67 | C1 |
43681 | 11^2 * 19^2 | -11, -19 | C1 |
71824 | 2^4 * 67^2 | -4, -67 | C1 |
90601 | 7^2 * 43^2 | -7, -43 | C1 |
118336 | 2^6 * 43^2 | -8, -43 | C1 |
239121 | 3^2 * 163^2 | -3, -163 | C1 |
287296 | 2^6 * 67^2 | -8, -67 | C1 |
425104 | 2^4 * 163^2 | -4, -163 | C1 |
543169 | 11^2 * 67^2 | -11, -67 | C1 |
1301881 | 7^2 * 163^2 | -7, -163 | C1 |
1620529 | 19^2 * 67^2 | -19, -67 | C1 |
3214849 | 11^2 * 163^2 | -11, -163 | C1 |
8300161 | 43^2 * 67^2 | -43, -67 | C1 |
9591409 | 19^2 * 163^2 | -19, -163 | C1 |
49126081 | 43^2 * 163^2 | -43, -163 | C1 |
119268241 | 67^2 * 163^2 | -67, -163 | C1 |
Die folgende Tabelle enthält alle imaginären biquadratischen Zahlkörper der Familie 2b mit Exponent 1.
Die Ergebnisse werden ohne Verwendung einer Vermutung bewiesen.
Diskriminante | Faktorisierung | Erzeuger | Klassengruppe |
225 | 3^2 * 5^2 | -3, 5 | C1 |
400 | 2^4 * 5^2 | -4, 5 | C1 |
576 | 2^6 * 3^2 | -3, 8 | C1 |
1225 | 5^2 * 7^2 | -7, 5 | C1 |
1600 | 2^6 * 5^2 | -8, 5 | C1 |
2601 | 3^2 * 17^2 | -3, 17 | C1 |
2704 | 2^4 * 13^2 | -4, 13 | C1 |
7744 | 2^6 * 11^2 | -11, 8 | C1 |
8281 | 7^2 * 13^2 | -7, 13 | C1 |
15129 | 3^2 * 41^2 | -3, 41 | C1 |
21904 | 2^4 * 37^2 | -4, 37 | C1 |
34969 | 11^2 * 17^2 | -11, 17 | C1 |
53824 | 2^6 * 29^2 | -8, 29 | C1 |
71289 | 3^2 * 89^2 | -3, 89 | C1 |
182329 | 7^2 * 61^2 | -7, 61 | C1 |
Exponent 3
Die folgende Tabelle enthält alle imaginären biquadratischen Zahlkörper der Familie 2a mit Exponent 3. Die Ergebnisse werden unter Verwendung von ERH für imaginärquadratische Zahlkörper bewiesen.
Diskriminante | Faktorisierung | Erzeuger | Klassengruppe |
4761 | 3^2 * 23^2 | -3, -23 | C3 |
8464 | 2^4 * 23^2 | -4, -23 | C3 |
8649 | 3^2 * 31^2 | -3, -31 | C3 |
15376 | 2^4 * 31^2 | -4, -31 | C3 |
25921 | 7^2 * 23^2 | -7, -23 | C3 |
31329 | 3^2 * 59^2 | -3, -59 | C3 |
33856 | 2^6 * 23^2 | -8, -23 | C3 |
47089 | 7^2 * 31^2 | -7, -31 | C3 |
55696 | 2^4 * 59^2 | -4, -59 | C3 |
61504 | 2^6 * 31^2 | -8, -31 | C3 |
62001 | 3^2 * 83^2 | -3, -83 | C3 |
64009 | 11^2 * 23^2 | -11, -23 | C3 |
103041 | 3^2 * 107^2 | -3, -107 | C3 x C3 |
110224 | 2^4 * 83^2 | -4, -83 | C3 |
116281 | 11^2 * 31^2 | -11, -31 | C3 |
170569 | 7^2 * 59^2 | -7, -59 | C3 |
173889 | 3^2 * 139^2 | -3, -139 | C3 |
183184 | 2^4 * 107^2 | -4, -107 | C3 |
190969 | 19^2 * 23^2 | -19, -23 | C3 |
219961 | 7^2 * 67^2 | -7, -67 | C3 |
222784 | 2^6 * 59^2 | -8, -59 | C3 |
223729 | 11^2 * 43^2 | -11, -43 | C3 |
309136 | 2^4 * 139^2 | -4, -139 | C3 |
337561 | 7^2 * 83^2 | -7, -83 | C3 |
346921 | 19^2 * 31^2 | -19, -31 | C3 |
400689 | 3^2 * 211^2 | -3, -211 | C3 |
421201 | 11^2 * 59^2 | -11, -59 | C3 |
440896 | 2^6 * 83^2 | -8, -83 | C3 |
508369 | 23^2 * 31^2 | -23, -31 | C3 x C3 |
561001 | 7^2 * 107^2 | -7, -107 | C3 |
712336 | 2^4 * 211^2 | -4, -211 | C3 |
720801 | 3^2 * 283^2 | -3, -283 | C3 |
732736 | 2^6 * 107^2 | -8, -107 | C3 |
833569 | 11^2 * 83^2 | -11, -83 | C3 |
848241 | 3^2 * 307^2 | -3, -307 | C3 |
946729 | 7^2 * 139^2 | -7, -139 | C3 |
978121 | 23^2 * 43^2 | -23, -43 | C3 |
986049 | 3^2 * 331^2 | -3, -331 | C3 x C3 |
1236544 | 2^6 * 139^2 | -8, -139 | C3 |
1256641 | 19^2 * 59^2 | -19, -59 | C3 |
1281424 | 2^4 * 283^2 | -4, -283 | C3 |
1292769 | 3^2 * 379^2 | -3, -379 | C3 |
1385329 | 11^2 * 107^2 | -11, -107 | C3 |
1507984 | 2^4 * 307^2 | -4, -307 | C3 |
1700416 | 2^6 * 163^2 | -8, -163 | C3 |
1752976 | 2^4 * 331^2 | -4, -331 | C3 |
1776889 | 31^2 * 43^2 | -31, -43 | C3 |
1841449 | 23^2 * 59^2 | -23, -59 | C3 x C3 |
2181529 | 7^2 * 211^2 | -7, -211 | C3 |
2241009 | 3^2 * 499^2 | -3, -499 | C3 |
2298256 | 2^4 * 379^2 | -4, -379 | C3 |
2337841 | 11^2 * 139^2 | -11, -139 | C3 |
2374681 | 23^2 * 67^2 | -23, -67 | C3 |
2486929 | 19^2 * 83^2 | -19, -83 | C3 |
2849344 | 2^6 * 211^2 | -8, -211 | C3 |
3345241 | 31^2 * 59^2 | -31, -59 | C3 x C3 |
3644281 | 23^2 * 83^2 | -23, -83 | C3 x C3 |
3721041 | 3^2 * 643^2 | -3, -643 | C3 x C3 |
3924361 | 7^2 * 283^2 | -7, -283 | C3 |
4133089 | 19^2 * 107^2 | -19, -107 | C3 |
4313929 | 31^2 * 67^2 | -31, -67 | C3 |
4618201 | 7^2 * 307^2 | -7, -307 | C3 |
4787344 | 2^4 * 547^2 | -4, -547 | C3 |
5125696 | 2^6 * 283^2 | -8, -283 | C3 |
5368489 | 7^2 * 331^2 | -7, -331 | C3 |
5387041 | 11^2 * 211^2 | -11, -211 | C3 |
6031936 | 2^6 * 307^2 | -8, -307 | C3 |
6056521 | 23^2 * 107^2 | -23, -107 | C3 x C3 |
6436369 | 43^2 * 59^2 | -43, -59 | C3 |
6615184 | 2^4 * 643^2 | -4, -643 | C3 |
6620329 | 31^2 * 83^2 | -31, -83 | C3 x C3 |
6974881 | 19^2 * 139^2 | -19, -139 | C3 |
7011904 | 2^6 * 331^2 | -8, -331 | C3 |
7017201 | 3^2 * 883^2 | -3, -883 | C3 |
7038409 | 7^2 * 379^2 | -7, -379 | C3 |
7403841 | 3^2 * 907^2 | -3, -907 | C3 |
9193024 | 2^6 * 379^2 | -8, -379 | C3 |
9690769 | 11^2 * 283^2 | -11, -283 | C3 |
10220809 | 23^2 * 139^2 | -23, -139 | C3 x C3 |
11002489 | 31^2 * 107^2 | -31, -107 | C3 x C3 |
11404129 | 11^2 * 307^2 | -11, -307 | C3 |
12201049 | 7^2 * 499^2 | -7, -499 | C3 |
12475024 | 2^4 * 883^2 | -4, -883 | C3 |
12737761 | 43^2 * 83^2 | -43, -83 | C3 x C3 |
13162384 | 2^4 * 907^2 | -4, -907 | C3 |
13256881 | 11^2 * 331^2 | -11, -331 | C3 |
14055001 | 23^2 * 163^2 | -23, -163 | C3 |
14661241 | 7^2 * 547^2 | -7, -547 | C3 |
15626209 | 59^2 * 67^2 | -59, -67 | C3 |
15936064 | 2^6 * 499^2 | -8, -499 | C3 |
17380561 | 11^2 * 379^2 | -11, -379 | C3 |
18567481 | 31^2 * 139^2 | -31, -139 | C3 x C3 |
19149376 | 2^6 * 547^2 | -8, -547 | C3 |
20259001 | 7^2 * 643^2 | -7, -643 | C3 |
21169201 | 43^2 * 107^2 | -43, -107 | C3 |
23551609 | 23^2 * 211^2 | -23, -211 | C3 x C3 x C3 |
23980609 | 59^2 * 83^2 | -59, -83 | C3 x C3 |
25532809 | 31^2 * 163^2 | -31, -163 | C3 |
26460736 | 2^6 * 643^2 | -8, -643 | C3 |
28912129 | 19^2 * 283^2 | -19, -283 | C3 |
30129121 | 11^2 * 499^2 | -11, -499 | C3 |
30924721 | 67^2 * 83^2 | -67, -83 | C3 |
34023889 | 19^2 * 307^2 | -19, -307 | C3 |
35724529 | 43^2 * 139^2 | -43, -139 | C3 |
36204289 | 11^2 * 547^2 | -11, -547 | C3 |
38204761 | 7^2 * 883^2 | -7, -883 | C3 |
39551521 | 19^2 * 331^2 | -19, -331 | C3 x C3 |
39853969 | 59^2 * 107^2 | -59, -107 | C3 x C3 |
40309801 | 7^2 * 907^2 | -7, -907 | C3 |
42367081 | 23^2 * 283^2 | -23, -283 | C3 x C3 |
42784681 | 31^2 * 211^2 | -31, -211 | C3 x C3 |
49857721 | 23^2 * 307^2 | -23, -307 | C3 x C3 |
50027329 | 11^2 * 643^2 | -11, -643 | C3 |
51394561 | 67^2 * 107^2 | -67, -107 | C3 |
51854401 | 19^2 * 379^2 | -19, -379 | C3 |
52649536 | 2^6 * 907^2 | -8, -907 | C3 |
57957769 | 23^2 * 331^2 | -23, -331 | C3 x C3 |
67256401 | 59^2 * 139^2 | -59, -139 | C3 x C3 |
75986089 | 23^2 * 379^2 | -23, -379 | C3 x C3 |
78872161 | 83^2 * 107^2 | -83, -107 | C3 x C3 |
82319329 | 43^2 * 211^2 | -43, -211 | C3 x C3 |
86731969 | 67^2 * 139^2 | -67, -139 | C3 |
89889361 | 19^2 * 499^2 | -19, -499 | C3 |
90573289 | 31^2 * 307^2 | -31, -307 | C3 x C3 x C3 |
92486689 | 59^2 * 163^2 | -59, -163 | C3 |
94342369 | 11^2 * 883^2 | -11, -883 | C3 |
99540529 | 11^2 * 907^2 | -11, -907 | C3 |
105288121 | 31^2 * 331^2 | -31, -331 | C3 x C3 x C3 |
108014449 | 19^2 * 547^2 | -19, -547 | C3 |
131721529 | 23^2 * 499^2 | -23, -499 | C3 x C3 |
138039001 | 31^2 * 379^2 | -31, -379 | C3 x C3 |
145950561 | 3^2 * 4027^2 | -3, -4027 | C3 x C3 x C3 |
148084561 | 43^2 * 283^2 | -43, -283 | C3 |
149255089 | 19^2 * 643^2 | -19, -643 | C3 |
154977601 | 59^2 * 211^2 | -59, -211 | C3 x C3 |
158281561 | 23^2 * 547^2 | -23, -547 | C3 x C3 |
174266401 | 43^2 * 307^2 | -43, -307 | C3 |
183033841 | 83^2 * 163^2 | -83, -163 | C3 |
199854769 | 67^2 * 211^2 | -67, -211 | C3 |
202578289 | 43^2 * 331^2 | -43, -331 | C3 |
218714521 | 23^2 * 643^2 | -23, -643 | C3 x C3 |
221206129 | 107^2 * 139^2 | -107, -139 | C3 x C3 |
239289961 | 31^2 * 499^2 | -31, -499 | C3 x C3 |
259467664 | 2^4 * 4027^2 | -4, -4027 | C3 x C3 |
265592209 | 43^2 * 379^2 | -43, -379 | C3 |
278789809 | 59^2 * 283^2 | -59, -283 | C3 x C3 |
281467729 | 19^2 * 883^2 | -19, -883 | C3 x C3 |
296976289 | 19^2 * 907^2 | -19, -907 | C3 |
304188481 | 107^2 * 163^2 | -107, -163 | C3 |
306705169 | 83^2 * 211^2 | -83, -211 | C3 x C3 |
328080769 | 59^2 * 307^2 | -59, -307 | C3 x C3 |
359519521 | 67^2 * 283^2 | -67, -283 | C3 |
381381841 | 59^2 * 331^2 | -59, -331 | C3 x C3 |
397324489 | 31^2 * 643^2 | -31, -643 | C3 x C3 |
412455481 | 23^2 * 883^2 | -23, -883 | C3 x C3 |
423083761 | 67^2 * 307^2 | -67, -307 | C3 |
435181321 | 23^2 * 907^2 | -23, -907 | C3 x C3 |
460402849 | 43^2 * 499^2 | -43, -499 | C3 |
491819329 | 67^2 * 331^2 | -67, -331 | C3 |
500014321 | 59^2 * 379^2 | -59, -379 | C3 x C3 |
509720929 | 107^2 * 211^2 | -107, -211 | C3 x C3 |
513339649 | 139^2 * 163^2 | -139, -163 | C3 |
551733121 | 83^2 * 283^2 | -83, -283 | C3 x C3 |
553237441 | 43^2 * 547^2 | -43, -547 | C3 |
644804449 | 67^2 * 379^2 | -67, -379 | C3 |
649281361 | 83^2 * 307^2 | -83, -307 | C3 x C3 |
749281129 | 31^2 * 883^2 | -31, -883 | C3 x C3 |
764467201 | 43^2 * 643^2 | -43, -643 | C3 |
790565689 | 31^2 * 907^2 | -31, -907 | C3 x C3 |
794619721 | 7^2 * 4027^2 | -7, -4027 | C3 x C3 |
860190241 | 139^2 * 211^2 | -139, -211 | C3 x C3 |
866772481 | 59^2 * 499^2 | -59, -499 | C3 x C3 |
916938961 | 107^2 * 283^2 | -107, -283 | C3 x C3 |
1037870656 | 2^6 * 4027^2 | -8, -4027 | C3 x C3 |
1041546529 | 59^2 * 547^2 | -59, -547 | C3 x C3 |
1079056801 | 107^2 * 307^2 | -107, -307 | C3 x C3 |
1117765489 | 67^2 * 499^2 | -67, -499 | C3 |
1182878449 | 163^2 * 211^2 | -163, -211 | C3 |
1254363889 | 107^2 * 331^2 | -107, -331 | C3 x C3 |
1343149201 | 67^2 * 547^2 | -67, -547 | C3 |
1439215969 | 59^2 * 643^2 | -59, -643 | C3 x C3 |
1441644961 | 43^2 * 883^2 | -43, -883 | C3 |
1521078001 | 43^2 * 907^2 | -43, -907 | C3 |
1547399569 | 139^2 * 283^2 | -139, -283 | C3 x C3 |
1644545809 | 107^2 * 379^2 | -107, -379 | C3 x C3 |
1715367889 | 83^2 * 499^2 | -83, -499 | C3 x C3 |
1820984929 | 139^2 * 307^2 | -139, -307 | C3 x C3 x C3 |
1855972561 | 67^2 * 643^2 | -67, -643 | C3 |
1962224209 | 11^2 * 4027^2 | -11, -4027 | C3 x C3 |
2061250801 | 83^2 * 547^2 | -83, -547 | C3 x C3 x C3 |
2116828081 | 139^2 * 331^2 | -139, -331 | C3 x C3 |
2127884641 | 163^2 * 283^2 | -163, -283 | C3 x C3 |
2714097409 | 59^2 * 883^2 | -59, -883 | C3 x C3 x C3 |
2775287761 | 139^2 * 379^2 | -139, -379 | C3 x C3 |
2848250161 | 83^2 * 643^2 | -83, -643 | C3 x C3 x C3 |
2850812449 | 107^2 * 499^2 | -107, -499 | C3 x C3 |
2863641169 | 59^2 * 907^2 | -59, -907 | C3 x C3 |
2910926209 | 163^2 * 331^2 | -163, -331 | C3 |
3500023921 | 67^2 * 883^2 | -67, -883 | C3 |
3565642369 | 211^2 * 283^2 | -211, -283 | C3 x C3 |
3692871361 | 67^2 * 907^2 | -67, -907 | C3 |
3816397729 | 163^2 * 379^2 | -163, -379 | C3 |
4196059729 | 211^2 * 307^2 | -211, -307 | C3 x C3 |
4733577601 | 107^2 * 643^2 | -107, -643 | C3 x C3 |
4810948321 | 139^2 * 499^2 | -139, -499 | C3 x C3 |
4877765281 | 211^2 * 331^2 | -211, -331 | C3 x C3 |
5371277521 | 83^2 * 883^2 | -83, -883 | C3 x C3 |
5667228961 | 83^2 * 907^2 | -83, -907 | C3 x C3 |
5781017089 | 139^2 * 547^2 | -139, -547 | C3 x C3 |
6395040961 | 211^2 * 379^2 | -211, -379 | C3 x C3 |
6615707569 | 163^2 * 499^2 | -163, -499 | C3 |
7548308161 | 283^2 * 307^2 | -283, -307 | C3 x C3 |
7949683921 | 163^2 * 547^2 | -163, -547 | C3 |
7988248129 | 139^2 * 643^2 | -139, -643 | C3 x C3 |
8578649641 | 23^2 * 4027^2 | -23, -4027 | C3 x C3 x C3 |
8774630929 | 283^2 * 331^2 | -283, -331 | C3 x C3 |
8926659361 | 107^2 * 883^2 | -107, -883 | C3 x C3 |
9418508401 | 107^2 * 907^2 | -107, -907 | C3 x C3 |
10326014689 | 307^2 * 331^2 | -307, -331 | C3 x C3 |
10984926481 | 163^2 * 643^2 | -163, -643 | C3 |
11085773521 | 211^2 * 499^2 | -211, -499 | C3 x C3 |
11504064049 | 283^2 * 379^2 | -283, -379 | C3 x C3 x C3 |
13321083889 | 211^2 * 547^2 | -211, -547 | C3 x C3 |
15064371169 | 139^2 * 883^2 | -139, -883 | C3 x C3 x C3 |
15584276569 | 31^2 * 4027^2 | -31, -4027 | C3 x C3 x C3 |
15737451601 | 331^2 * 379^2 | -331, -379 | C3 x C3 |
15894401329 | 139^2 * 907^2 | -139, -907 | C3 x C3 |
18407162929 | 211^2 * 643^2 | -211, -643 | C3 x C3 x C3 |
19942241089 | 283^2 * 499^2 | -283, -499 | C3 x C3 x C3 |
20715557041 | 163^2 * 883^2 | -163, -883 | C3 |
23468095249 | 307^2 * 499^2 | -307, -499 | C3 x C3 x C3 |
23963349601 | 283^2 * 547^2 | -283, -547 | C3 x C3 |
27280798561 | 331^2 * 499^2 | -331, -499 | C3 x C3 |
28200149041 | 307^2 * 547^2 | -307, -547 | C3 x C3 |
29984731921 | 43^2 * 4027^2 | -43, -4027 | C3 x C3 |
32781637249 | 331^2 * 547^2 | -331, -547 | C3 x C3 |
34712533969 | 211^2 * 883^2 | -211, -883 | C3 x C3 |
35766752641 | 379^2 * 499^2 | -379, -499 | C3 x C3 |
36625156129 | 211^2 * 907^2 | -211, -907 | C3 x C3 |
38967154801 | 307^2 * 643^2 | -307, -643 | C3 x C3 x C3 |
42978679969 | 379^2 * 547^2 | -379, -547 | C3 x C3 |
45297885889 | 331^2 * 643^2 | -331, -643 | C3 x C3 |
56450433649 | 59^2 * 4027^2 | -59, -4027 | C3 x C3 x C3 |
59388227809 | 379^2 * 643^2 | -379, -643 | C3 x C3 |
62444512321 | 283^2 * 883^2 | -283, -883 | C3 x C3 |
65885135761 | 283^2 * 907^2 | -283, -907 | C3 x C3 |
72796896481 | 67^2 * 4027^2 | -67, -4027 | C3 x C3 |
73484908561 | 307^2 * 883^2 | -307, -883 | C3 x C3 |
74503340209 | 499^2 * 547^2 | -499, -547 | C3 x C3 |
77533845601 | 307^2 * 907^2 | -307, -907 | C3 x C3 x C3 |
85423506529 | 331^2 * 883^2 | -331, -883 | C3 x C3 |
90130247089 | 331^2 * 907^2 | -331, -907 | C3 x C3 |
102949214449 | 499^2 * 643^2 | -499, -643 | C3 x C3 |
111717046081 | 83^2 * 4027^2 | -83, -4027 | C3 x C3 x C3 |
118166125009 | 379^2 * 907^2 | -379, -907 | C3 x C3 |
123707661841 | 547^2 * 643^2 | -547, -643 | C3 x C3 |
185665330321 | 107^2 * 4027^2 | -107, -4027 | C3 x C3 x C3 |
194143340689 | 499^2 * 883^2 | -499, -883 | C3 x C3 |
204840423649 | 499^2 * 907^2 | -499, -907 | C3 x C3 |
233289966001 | 547^2 * 883^2 | -547, -883 | C3 x C3 |
246143984641 | 547^2 * 907^2 | -547, -907 | C3 x C3 x C3 |
322361637361 | 643^2 * 883^2 | -643, -883 | C3 x C3 |
340123406401 | 643^2 * 907^2 | -643, -907 | C3 x C3 |
430862272801 | 163^2 * 4027^2 | -163, -4027 | C3 x C3 |
641410376161 | 883^2 * 907^2 | -883, -907 | C3 x C3 x C3 |
721984991809 | 211^2 * 4027^2 | -211, -4027 | C3 x C3 x C3 |
1298781608881 | 283^2 * 4027^2 | -283, -4027 | C3 x C3 x C3 |
1528410491521 | 307^2 * 4027^2 | -307, -4027 | C3 x C3 x C3 |
1776721045969 | 331^2 * 4027^2 | -331, -4027 | C3 x C3 x C3 |
2329387170289 | 379^2 * 4027^2 | -379, -4027 | C3 x C3 x C3 |
4037981737729 | 499^2 * 4027^2 | -499, -4027 | C3 x C3 x C3 |
4852191267361 | 547^2 * 4027^2 | -547, -4027 | C3 x C3 x C3 |
6704790388321 | 643^2 * 4027^2 | -643, -4027 | C3 x C3 x C3 x C3 |
12644005217281 | 883^2 * 4027^2 | -883, -4027 | C3 x C3 x C3 |
13340675895121 | 907^2 * 4027^2 | -907, -4027 | C3 x C3 x C3 |
Die folgende Tabelle enthält alle imaginären biquadratischen Zahlkörper der Familie 2b mit Exponent 3. Die Ergebnisse werden unter Verwendung von ERH für imaginärquadratische Zahlenkörper bewiesen.
Diskriminante | Faktorisierung | Erzeuger | Klassengruppe |
7569 | 3^2 * 29^2 | -3, 29 | C3 |
10816 | 2^6 * 13^2 | -8, 13 | C3 |
13225 | 5^2 * 23^2 | -23, 5 | C3 |
13456 | 2^4 * 29^2 | -4, 29 | C3 |
23104 | 2^6 * 19^2 | -19, 8 | C3 |
44944 | 2^4 * 53^2 | -4, 53 | C3 |
59536 | 2^4 * 61^2 | -4, 61 | C3 |
61009 | 13^2 * 19^2 | -19, 13 | C3 |
114921 | 3^2 * 113^2 | -3, 113 | C3 |
162409 | 13^2 * 31^2 | -31, 13 | C3 |
168921 | 3^2 * 137^2 | -3, 137 | C3 |
179776 | 2^6 * 53^2 | -8, 53 | C3 |
190096 | 2^4 * 109^2 | -4, 109 | C3 |
203401 | 11^2 * 41^2 | -11, 41 | C3 |
222784 | 2^6 * 59^2 | -59, 8 | C3 x C3 |
394384 | 2^4 * 157^2 | -4, 157 | C3 |
499849 | 7^2 * 101^2 | -7, 101 | C3 |
594441 | 3^2 * 257^2 | -3, 257 | C3 x C3 |
652864 | 2^6 * 101^2 | -8, 101 | C3 |
710649 | 3^2 * 281^2 | -3, 281 | C3 |
732736 | 2^6 * 107^2 | -107, 8 | C3 x C3 |
1121481 | 3^2 * 353^2 | -3, 353 | C3 |
1207801 | 7^2 * 157^2 | -7, 157 | C3 |
1227664 | 2^4 * 277^2 | -4, 277 | C3 |
1315609 | 31^2 * 37^2 | -31, 37 | C3 x C3 |
1420864 | 2^6 * 149^2 | -8, 149 | C3 |
1485961 | 23^2 * 53^2 | -23, 53 | C3 x C3 |
1605289 | 7^2 * 181^2 | -7, 181 | C3 |
1814409 | 3^2 * 449^2 | -3, 449 | C3 |
2442969 | 3^2 * 521^2 | -3, 521 | C3 |
2521744 | 2^4 * 397^2 | -4, 397 | C3 |
2569609 | 7^2 * 229^2 | -7, 229 | C3 x C3 |
3396649 | 19^2 * 97^2 | -19, 97 | C3 |
5212089 | 3^2 * 761^2 | -3, 761 | C3 x C3 |
5968249 | 7^2 * 349^2 | -7, 349 | C3 |
6568969 | 11^2 * 233^2 | -11, 233 | C3 |
7767369 | 3^2 * 929^2 | -3, 929 | C3 |
11744329 | 23^2 * 149^2 | -23, 149 | C3 x C3 |
95023504 | 2^4 * 2437^2 | -4, 2437 | C3 x C3 |
145612489 | 11^2 * 1097^2 | -11, 1097 | C3 x C3 |
386161801 | 43^2 * 457^2 | -43, 457 | C3 x C3 |
503688249 | 3^2 * 7481^2 | -3, 7481 | C3 x C3 x C3 |
1157836729 | 7^2 * 4861^2 | -7, 4861 | C3 x C3 |
Exponent 5
Die folgende Tabelle enthält alle imaginären biquadratischen Zahlkörper der Familie 2a mit Exponent 5. Die Ergebnisse werden unter Verwendung von ERH für imaginärquadratische Zahlkörper bewiesen.
Diskriminante | Faktorisierung | Erzeuger | Klassengruppe |
19881 | 3^2 * 47^2 | -3, -47 | C5 |
35344 | 2^4 * 47^2 | -4, -47 | C5 |
56169 | 3^2 * 79^2 | -3, -79 | C5 |
95481 | 3^2 * 103^2 | -3, -103 | C5 |
108241 | 7^2 * 47^2 | -7, -47 | C5 |
141376 | 2^6 * 47^2 | -8, -47 | C5 |
145161 | 3^2 * 127^2 | -3, -127 | C5 |
154449 | 3^2 * 131^2 | -3, -131 | C5 |
169744 | 2^4 * 103^2 | -4, -103 | C5 |
258064 | 2^4 * 127^2 | -4, -127 | C5 |
267289 | 11^2 * 47^2 | -11, -47 | C5 |
274576 | 2^4 * 131^2 | -4, -131 | C5 |
288369 | 3^2 * 179^2 | -3, -179 | C5 |
305809 | 7^2 * 79^2 | -7, -79 | C5 |
399424 | 2^6 * 79^2 | -8, -79 | C5 |
463761 | 3^2 * 227^2 | -3, -227 | C5 |
512656 | 2^4 * 179^2 | -4, -179 | C5 |
519841 | 7^2 * 103^2 | -7, -103 | C5 |
667489 | 19^2 * 43^2 | -19, -43 | C5 |
678976 | 2^6 * 103^2 | -8, -103 | C5 |
755161 | 11^2 * 79^2 | -11, -79 | C5 |
790321 | 7^2 * 127^2 | -7, -127 | C5 |
797449 | 19^2 * 47^2 | -19, -47 | C5 |
824464 | 2^4 * 227^2 | -4, -227 | C5 |
840889 | 7^2 * 131^2 | -7, -131 | C5 |
1083681 | 3^2 * 347^2 | -3, -347 | C5 |
1098304 | 2^6 * 131^2 | -8, -131 | C5 |
1283689 | 11^2 * 103^2 | -11, -103 | C5 |
1570009 | 7^2 * 179^2 | -7, -179 | C5 |
1766241 | 3^2 * 443^2 | -3, -443 | C5 |
1926544 | 2^4 * 347^2 | -4, -347 | C5 |
1951609 | 11^2 * 127^2 | -11, -127 | C5 |
2050624 | 2^6 * 179^2 | -8, -179 | C5 |
2076481 | 11^2 * 131^2 | -11, -131 | C5 |
2253001 | 19^2 * 79^2 | -19, -79 | C5 |
2461761 | 3^2 * 523^2 | -3, -523 | C5 |
2524921 | 7^2 * 227^2 | -7, -227 | C5 |
2934369 | 3^2 * 571^2 | -3, -571 | C5 |
3297856 | 2^6 * 227^2 | -8, -227 | C5 |
3448449 | 3^2 * 619^2 | -3, -619 | C5 |
3876961 | 11^2 * 179^2 | -11, -179 | C5 |
4198401 | 3^2 * 683^2 | -3, -683 | C5 |
4297329 | 3^2 * 691^2 | -3, -691 | C5 |
4376464 | 2^4 * 523^2 | -4, -523 | C5 |
4915089 | 3^2 * 739^2 | -3, -739 | C5 |
5216656 | 2^4 * 571^2 | -4, -571 | C5 |
5574321 | 3^2 * 787^2 | -3, -787 | C5 |
5822569 | 19^2 * 127^2 | -19, -127 | C5 |
6130576 | 2^4 * 619^2 | -4, -619 | C5 |
6195121 | 19^2 * 131^2 | -19, -131 | C5 |
6235009 | 11^2 * 227^2 | -11, -227 | C5 |
7463824 | 2^4 * 683^2 | -4, -683 | C5 |
7639696 | 2^4 * 691^2 | -4, -691 | C5 |
7706176 | 2^6 * 347^2 | -8, -347 | C5 |
8071281 | 3^2 * 947^2 | -3, -947 | C5 |
8737936 | 2^4 * 739^2 | -4, -739 | C5 |
9616201 | 7^2 * 443^2 | -7, -443 | C5 |
9909904 | 2^4 * 787^2 | -4, -787 | C5 |
9916201 | 47^2 * 67^2 | -47, -67 | C5 |
9941409 | 3^2 * 1051^2 | -3, -1051 | C5 |
11350161 | 3^2 * 1123^2 | -3, -1123 | C5 |
11539609 | 43^2 * 79^2 | -43, -79 | C5 |
11566801 | 19^2 * 179^2 | -19, -179 | C5 |
12559936 | 2^6 * 443^2 | -8, -443 | C5 |
13402921 | 7^2 * 523^2 | -7, -523 | C5 |
13786369 | 47^2 * 79^2 | -47, -79 | C5 x C5 |
14348944 | 2^4 * 947^2 | -4, -947 | C5 |
14569489 | 11^2 * 347^2 | -11, -347 | C5 |
15976009 | 7^2 * 571^2 | -7, -571 | C5 x C5 |
17505856 | 2^6 * 523^2 | -8, -523 | C5 |
17673616 | 2^4 * 1051^2 | -4, -1051 | C5 |
18601969 | 19^2 * 227^2 | -19, -227 | C5 |
18774889 | 7^2 * 619^2 | -7, -619 | C5 |
19616041 | 43^2 * 103^2 | -43, -103 | C5 |
20178064 | 2^4 * 1123^2 | -4, -1123 | C5 |
20866624 | 2^6 * 571^2 | -8, -571 | C5 |
22857961 | 7^2 * 683^2 | -7, -683 | C5 |
23396569 | 7^2 * 691^2 | -7, -691 | C5 |
23746129 | 11^2 * 443^2 | -11, -443 | C5 |
24522304 | 2^6 * 619^2 | -8, -619 | C5 |
26718561 | 3^2 * 1723^2 | -3, -1723 | C5 |
26759929 | 7^2 * 739^2 | -7, -739 | C5 |
27468081 | 3^2 * 1747^2 | -3, -1747 | C5 x C5 |
28015849 | 67^2 * 79^2 | -67, -79 | C5 |
29822521 | 43^2 * 127^2 | -43, -127 | C5 |
29855296 | 2^6 * 683^2 | -8, -683 | C5 |
30349081 | 7^2 * 787^2 | -7, -787 | C5 |
30558784 | 2^6 * 691^2 | -8, -691 | C5 |
31371201 | 3^2 * 1867^2 | -3, -1867 | C5 |
31730689 | 43^2 * 131^2 | -43, -131 | C5 |
33097009 | 11^2 * 523^2 | -11, -523 | C5 |
35628961 | 47^2 * 127^2 | -47, -127 | C5 x C5 |
37908649 | 47^2 * 131^2 | -47, -131 | C5 x C5 x C5 |
39450961 | 11^2 * 571^2 | -11, -571 | C5 |
39639616 | 2^6 * 787^2 | -8, -787 | C5 |
43467649 | 19^2 * 347^2 | -19, -347 | C5 |
43678881 | 3^2 * 2203^2 | -3, -2203 | C5 |
43943641 | 7^2 * 947^2 | -7, -947 | C5 |
47499664 | 2^4 * 1723^2 | -4, -1723 | C5 |
48832144 | 2^4 * 1747^2 | -4, -1747 | C5 |
49575681 | 3^2 * 2347^2 | -3, -2347 | C5 |
54125449 | 7^2 * 1051^2 | -7, -1051 | C5 |
55771024 | 2^4 * 1867^2 | -4, -1867 | C5 |
56445169 | 11^2 * 683^2 | -11, -683 | C5 x C5 |
57395776 | 2^6 * 947^2 | -8, -947 | C5 |
58690921 | 47^2 * 163^2 | -47, -163 | C5 |
59243809 | 43^2 * 179^2 | -43, -179 | C5 |
61795321 | 7^2 * 1123^2 | -7, -1123 | C5 x C5 |
64786401 | 3^2 * 2683^2 | -3, -2683 | C5 x C5 |
66080641 | 11^2 * 739^2 | -11, -739 | C5 |
66210769 | 79^2 * 103^2 | -79, -103 | C5 x C5 |
70694464 | 2^6 * 1051^2 | -8, -1051 | C5 |
70778569 | 47^2 * 179^2 | -47, -179 | C5 x C5 |
70845889 | 19^2 * 443^2 | -19, -443 | C5 |
72403081 | 67^2 * 127^2 | -67, -127 | C5 |
74943649 | 11^2 * 787^2 | -11, -787 | C5 |
77035729 | 67^2 * 131^2 | -67, -131 | C5 |
77651344 | 2^4 * 2203^2 | -4, -2203 | C5 |
80712256 | 2^6 * 1123^2 | -8, -1123 | C5 |
88134544 | 2^4 * 2347^2 | -4, -2347 | C5 |
95277121 | 43^2 * 227^2 | -43, -227 | C5 |
100661089 | 79^2 * 127^2 | -79, -127 | C5 x C5 |
107101801 | 79^2 * 131^2 | -79, -131 | C5 x C5 |
108513889 | 11^2 * 947^2 | -11, -947 | C5 |
113827561 | 47^2 * 227^2 | -47, -227 | C5 x C5 |
115175824 | 2^4 * 2683^2 | -4, -2683 | C5 |
117700801 | 19^2 * 571^2 | -19, -571 | C5 |
133656721 | 11^2 * 1051^2 | -11, -1051 | C5 |
138321121 | 19^2 * 619^2 | -19, -619 | C5 |
143832049 | 67^2 * 179^2 | -67, -179 | C5 |
145467721 | 7^2 * 1723^2 | -7, -1723 | C5 |
149548441 | 7^2 * 1747^2 | -7, -1747 | C5 |
152596609 | 11^2 * 1123^2 | -11, -1123 | C5 |
165817129 | 79^2 * 163^2 | -79, -163 | C5 |
171112561 | 103^2 * 127^2 | -103, -127 | C5 x C5 |
172370641 | 19^2 * 691^2 | -19, -691 | C5 |
182061049 | 103^2 * 131^2 | -103, -131 | C5 x C5 |
189998656 | 2^6 * 1723^2 | -8, -1723 | C5 |
195328576 | 2^6 * 1747^2 | -8, -1747 | C5 |
197149681 | 19^2 * 739^2 | -19, -739 | C5 |
222636241 | 43^2 * 347^2 | -43, -347 | C5 |
223084096 | 2^6 * 1867^2 | -8, -1867 | C5 |
223592209 | 19^2 * 787^2 | -19, -787 | C5 |
231313681 | 67^2 * 227^2 | -67, -227 | C5 |
237807241 | 7^2 * 2203^2 | -7, -2203 | C5 |
265983481 | 47^2 * 347^2 | -47, -347 | C5 x C5 |
269912041 | 7^2 * 2347^2 | -7, -2347 | C5 |
276789769 | 127^2 * 131^2 | -127, -131 | C5 x C5 x C5 |
281870521 | 103^2 * 163^2 | -103, -163 | C5 |
310605376 | 2^6 * 2203^2 | -8, -2203 | C5 |
321592489 | 79^2 * 227^2 | -79, -227 | C5 x C5 |
323748049 | 19^2 * 947^2 | -19, -947 | C5 |
339922969 | 103^2 * 179^2 | -103, -179 | C5 x C5 |
352538176 | 2^6 * 2347^2 | -8, -2347 | C5 |
352725961 | 7^2 * 2683^2 | -7, -2683 | C5 |
359216209 | 11^2 * 1723^2 | -11, -1723 | C5 |
362864401 | 43^2 * 443^2 | -43, -443 | C5 |
369293089 | 11^2 * 1747^2 | -11, -1747 | C5 |
398760961 | 19^2 * 1051^2 | -19, -1051 | C5 |
421768369 | 11^2 * 1867^2 | -11, -1867 | C5 |
428531401 | 127^2 * 163^2 | -127, -163 | C5 |
433514041 | 47^2 * 443^2 | -47, -443 | C5 x C5 |
455950609 | 131^2 * 163^2 | -131, -163 | C5 |
460703296 | 2^6 * 2683^2 | -8, -2683 | C5 |
505755121 | 43^2 * 523^2 | -43, -523 | C5 |
516789289 | 127^2 * 179^2 | -127, -179 | C5 x C5 |
546671161 | 103^2 * 227^2 | -103, -227 | C5 x C5 |
549855601 | 131^2 * 179^2 | -131, -179 | C5 x C5 |
587238289 | 11^2 * 2203^2 | -11, -2203 | C5 |
602849809 | 43^2 * 571^2 | -43, -571 | C5 |
604225561 | 47^2 * 523^2 | -47, -523 | C5 x C5 |
666517489 | 11^2 * 2347^2 | -11, -2347 | C5 |
720224569 | 47^2 * 571^2 | -47, -571 | C5 x C5 |
751472569 | 79^2 * 347^2 | -79, -347 | C5 x C5 |
831111241 | 127^2 * 227^2 | -127, -227 | C5 x C5 |
846402649 | 47^2 * 619^2 | -47, -619 | C5 x C5 |
851297329 | 163^2 * 179^2 | -163, -179 | C5 |
862538161 | 43^2 * 683^2 | -43, -683 | C5 x C5 |
871017169 | 11^2 * 2683^2 | -11, -2683 | C5 |
882862369 | 43^2 * 691^2 | -43, -691 | C5 |
884289169 | 131^2 * 227^2 | -131, -227 | C5 x C5 |
1009777729 | 43^2 * 739^2 | -43, -739 | C5 |
1030474201 | 47^2 * 683^2 | -47, -683 | C5 x C5 |
1054755529 | 47^2 * 691^2 | -47, -691 | C5 x C5 |
1101775249 | 19^2 * 1747^2 | -19, -1747 | C5 |
1145213281 | 43^2 * 787^2 | -43, -787 | C5 |
1206381289 | 47^2 * 739^2 | -47, -739 | C5 x C5 |
1224790009 | 79^2 * 443^2 | -79, -443 | C5 x C5 |
1277419081 | 103^2 * 347^2 | -103, -347 | C5 x C5 |
1368186121 | 47^2 * 787^2 | -47, -787 | C5 x C5 |
1369074001 | 163^2 * 227^2 | -163, -227 | C5 |
1463598049 | 67^2 * 571^2 | -67, -571 | C5 |
1651040689 | 179^2 * 227^2 | -179, -227 | C5 x C5 |
1658199841 | 43^2 * 947^2 | -43, -947 | C5 |
1707094489 | 79^2 * 523^2 | -79, -523 | C5 x C5 |
1720009729 | 67^2 * 619^2 | -67, -619 | C5 |
1752008449 | 19^2 * 2203^2 | -19, -2203 | C5 |
1942076761 | 127^2 * 347^2 | -127, -347 | C5 x C5 |
1981051081 | 47^2 * 947^2 | -47, -947 | C5 x C5 |
1988535649 | 19^2 * 2347^2 | -19, -2347 | C5 |
2034821881 | 79^2 * 571^2 | -79, -571 | C5 x C5 |
2082005641 | 103^2 * 443^2 | -103, -443 | C5 x C5 |
2094069121 | 67^2 * 683^2 | -67, -683 | C5 |
2143412209 | 67^2 * 691^2 | -67, -691 | C5 |
2331827521 | 43^2 * 1123^2 | -43, -1123 | C5 |
2391307801 | 79^2 * 619^2 | -79, -619 | C5 x C5 |
2451537169 | 67^2 * 739^2 | -67, -739 | C5 |
2480438416 | 2^4 * 12451^2 | -4, -12451 | C5 x C5 |
2598654529 | 19^2 * 2683^2 | -19, -2683 | C5 |
2780347441 | 67^2 * 787^2 | -67, -787 | C5 |
2785833961 | 47^2 * 1123^2 | -47, -1123 | C5 x C5 |
2901869161 | 103^2 * 523^2 | -103, -523 | C5 x C5 |
2911357849 | 79^2 * 683^2 | -79, -683 | C5 x C5 |
2979958921 | 79^2 * 691^2 | -79, -691 | C5 x C5 |
3165300121 | 127^2 * 443^2 | -127, -443 | C5 x C5 |
3199146721 | 163^2 * 347^2 | -163, -347 | C5 |
3367829089 | 131^2 * 443^2 | -131, -443 | C5 x C5 |
3408341161 | 79^2 * 739^2 | -79, -739 | C5 x C5 |
3458968969 | 103^2 * 571^2 | -103, -571 | C5 x C5 |
3865481929 | 79^2 * 787^2 | -79, -787 | C5 x C5 |
4025775601 | 67^2 * 947^2 | -67, -947 | C5 |
4064955049 | 103^2 * 619^2 | -103, -619 | C5 x C5 |
4411749241 | 127^2 * 523^2 | -127, -523 | C5 x C5 |
5065595929 | 103^2 * 691^2 | -103, -691 | C5 x C5 |
5214139681 | 163^2 * 443^2 | -163, -443 | C5 |
5595189601 | 131^2 * 571^2 | -131, -571 | C5 x C5 |
5596984969 | 79^2 * 947^2 | -79, -947 | C5 x C5 |
5643164641 | 43^2 * 1747^2 | -43, -1747 | C5 |
5661208081 | 67^2 * 1123^2 | -67, -1123 | C5 |
5793797689 | 103^2 * 739^2 | -103, -739 | C5 x C5 x C5 |
6204555361 | 227^2 * 347^2 | -227, -347 | C5 x C5 |
6288014209 | 179^2 * 443^2 | -179, -443 | C5 x C5 x C5 |
6445038961 | 43^2 * 1867^2 | -43, -1867 | C5 |
6557922361 | 47^2 * 1723^2 | -47, -1723 | C5 x C5 |
6570885721 | 103^2 * 787^2 | -103, -787 | C5 x C5 |
6575425921 | 131^2 * 619^2 | -131, -619 | C5 x C5 |
6741887881 | 47^2 * 1747^2 | -47, -1747 | C5 x C5 |
6893814841 | 79^2 * 1051^2 | -79, -1051 | C5 x C5 x C5 |
7267392001 | 163^2 * 523^2 | -163, -523 | C5 |
7524001081 | 127^2 * 683^2 | -127, -683 | C5 x C5 |
7596342649 | 7^2 * 12451^2 | -7, -12451 | C5 x C5 |
7699887001 | 47^2 * 1867^2 | -47, -1867 | C5 x C5 |
7870706089 | 79^2 * 1123^2 | -79, -1123 | C5 x C5 |
8005417729 | 131^2 * 683^2 | -131, -683 | C5 x C5 |
8194051441 | 131^2 * 691^2 | -131, -691 | C5 x C5 |
8662583329 | 163^2 * 571^2 | -163, -571 | C5 |
8764142689 | 179^2 * 523^2 | -179, -523 | C5 x C5 |
8808385609 | 127^2 * 739^2 | -127, -739 | C5 x C5 |
8973583441 | 43^2 * 2203^2 | -43, -2203 | C5 |
9371982481 | 131^2 * 739^2 | -131, -739 | C5 x C5 |
9514246681 | 103^2 * 947^2 | -103, -947 | C5 x C5 |
9921753664 | 2^6 * 12451^2 | -8, -12451 | C5 x C5 |
9989802601 | 127^2 * 787^2 | -127, -787 | C5 x C5 |
10112514721 | 227^2 * 443^2 | -227, -443 | C5 x C5 |
10180204609 | 163^2 * 619^2 | -163, -619 | C5 |
10185048241 | 43^2 * 2347^2 | -43, -2347 | C5 |
10446679681 | 179^2 * 571^2 | -179, -571 | C5 x C5 |
10628991409 | 131^2 * 787^2 | -131, -787 | C5 x C5 |
10720738681 | 47^2 * 2203^2 | -47, -2203 | C5 x C5 x C5 |
11718712009 | 103^2 * 1051^2 | -103, -1051 | C5 x C5 |
12168075481 | 47^2 * 2347^2 | -47, -2347 | C5 x C5 |
12276861601 | 179^2 * 619^2 | -179, -619 | C5 x C5 |
12563943921 | 3^2 * 37363^2 | -3, -37363 | C5 x C5 |
12686192689 | 163^2 * 691^2 | -163, -691 | C5 |
13310006161 | 43^2 * 2683^2 | -43, -2683 | C5 |
13326624481 | 67^2 * 1723^2 | -67, -1723 | C5 |
13379317561 | 103^2 * 1123^2 | -103, -1123 | C5 x C5 |
13700468401 | 67^2 * 1747^2 | -67, -1747 | C5 |
14464632361 | 127^2 * 947^2 | -127, -947 | C5 x C5 |
14509888849 | 163^2 * 739^2 | -163, -739 | C5 |
14946774049 | 179^2 * 683^2 | -179, -683 | C5 x C5 x C5 |
15298968721 | 179^2 * 691^2 | -179, -691 | C5 x C5 |
15390139249 | 131^2 * 947^2 | -131, -947 | C5 x C5 |
15647257921 | 67^2 * 1867^2 | -67, -1867 | C5 |
15901462201 | 47^2 * 2683^2 | -47, -2683 | C5 x C5 |
16456014961 | 163^2 * 787^2 | -163, -787 | C5 |
16800566689 | 227^2 * 571^2 | -227, -571 | C5 x C5 |
17498262961 | 179^2 * 739^2 | -179, -739 | C5 x C5 |
17816109529 | 127^2 * 1051^2 | -127, -1051 | C5 x C5 |
18527837689 | 79^2 * 1723^2 | -79, -1723 | C5 x C5 |
18758315521 | 11^2 * 12451^2 | -11, -12451 | C5 x C5 |
18956057761 | 131^2 * 1051^2 | -131, -1051 | C5 x C5 |
19047588169 | 79^2 * 1747^2 | -79, -1747 | C5 x C5 |
19743903169 | 227^2 * 619^2 | -227, -619 | C5 x C5 |
20340749641 | 127^2 * 1123^2 | -127, -1123 | C5 x C5 |
21642234769 | 131^2 * 1123^2 | -131, -1123 | C5 x C5 |
22335900304 | 2^4 * 37363^2 | -4, -37363 | C5 x C5 |
23630145841 | 347^2 * 443^2 | -347, -443 | C5 x C5 |
23827318321 | 163^2 * 947^2 | -163, -947 | C5 |
24604118449 | 227^2 * 691^2 | -227, -691 | C5 x C5 |
24727248001 | 67^2 * 2347^2 | -67, -2347 | C5 |
28141069009 | 227^2 * 739^2 | -227, -739 | C5 x C5 |
28734657169 | 179^2 * 947^2 | -179, -947 | C5 x C5 |
29348143969 | 163^2 * 1051^2 | -163, -1051 | C5 |
30288877369 | 79^2 * 2203^2 | -79, -2203 | C5 x C5 |
31495245961 | 103^2 * 1723^2 | -103, -1723 | C5 x C5 |
31915465201 | 227^2 * 787^2 | -227, -787 | C5 x C5 |
32378763481 | 103^2 * 1747^2 | -103, -1747 | C5 x C5 |
32935353361 | 347^2 * 523^2 | -347, -523 | C5 x C5 |
33506936401 | 163^2 * 1123^2 | -163, -1123 | C5 |
34377980569 | 79^2 * 2347^2 | -79, -2347 | C5 x C5 |
35392520641 | 179^2 * 1051^2 | -179, -1051 | C5 x C5 |
36979674601 | 103^2 * 1867^2 | -103, -1867 | C5 x C5 |
40407834289 | 179^2 * 1123^2 | -179, -1123 | C5 x C5 x C5 |
46211670961 | 227^2 * 947^2 | -227, -947 | C5 x C5 x C5 |
47882630041 | 127^2 * 1723^2 | -127, -1723 | C5 x C5 |
49225853161 | 127^2 * 1747^2 | -127, -1747 | C5 x C5 |
50946358369 | 131^2 * 1723^2 | -131, -1723 | C5 x C5 x C5 |
51487694281 | 103^2 * 2203^2 | -103, -2203 | C5 x C5 |
52375526449 | 131^2 * 1747^2 | -131, -1747 | C5 x C5 |
53679792721 | 443^2 * 523^2 | -443, -523 | C5 x C5 |
55964891761 | 19^2 * 12451^2 | -19, -12451 | C5 x C5 |
56169474001 | 347^2 * 683^2 | -347, -683 | C5 x C5 |
56918984929 | 227^2 * 1051^2 | -227, -1051 | C5 x C5 |
57493009729 | 347^2 * 691^2 | -347, -691 | C5 x C5 |
58438711081 | 103^2 * 2347^2 | -103, -2347 | C5 x C5 |
59817908929 | 131^2 * 1867^2 | -131, -1867 | C5 x C5 |
63985220209 | 443^2 * 571^2 | -443, -571 | C5 x C5 |
65757883489 | 347^2 * 739^2 | -347, -739 | C5 x C5 |
68403694681 | 7^2 * 37363^2 | -7, -37363 | C5 x C5 |
74577601921 | 347^2 * 787^2 | -347, -787 | C5 x C5 |
76368769801 | 103^2 * 2683^2 | -103, -2683 | C5 x C5 |
78277407961 | 127^2 * 2203^2 | -127, -2203 | C5 x C5 |
78876160801 | 163^2 * 1723^2 | -163, -1723 | C5 |
81088827121 | 163^2 * 1747^2 | -163, -1747 | C5 |
83285919649 | 131^2 * 2203^2 | -131, -2203 | C5 x C5 |
88845128761 | 127^2 * 2347^2 | -127, -2347 | C5 x C5 |
89181668689 | 523^2 * 571^2 | -523, -571 | C5 x C5 |
89343601216 | 2^6 * 37363^2 | -8, -37363 | C5 x C5 |
91547999761 | 443^2 * 683^2 | -443, -683 | C5 x C5 |
92611271041 | 163^2 * 1867^2 | -163, -1867 | C5 |
93705168769 | 443^2 * 691^2 | -443, -691 | C5 x C5 |
94529806849 | 131^2 * 2347^2 | -131, -2347 | C5 x C5 |
97789420369 | 179^2 * 1747^2 | -179, -1747 | C5 x C5 |
104805645169 | 523^2 * 619^2 | -523, -619 | C5 x C5 |
107175700129 | 443^2 * 739^2 | -443, -739 | C5 x C5 |
111684961249 | 179^2 * 1867^2 | -179, -1867 | C5 x C5 |
121550546881 | 443^2 * 787^2 | -443, -787 | C5 x C5 |
123533269729 | 131^2 * 2683^2 | -131, -2683 | C5 x C5 |
124926195601 | 571^2 * 619^2 | -571, -619 | C5 x C5 |
127598269681 | 523^2 * 683^2 | -523, -683 | C5 x C5 |
128944909921 | 163^2 * 2203^2 | -163, -2203 | C5 |
130604900449 | 523^2 * 691^2 | -523, -691 | C5 x C5 |
133003901809 | 347^2 * 1051^2 | -347, -1051 | C5 x C5 x C5 |
146352918721 | 163^2 * 2347^2 | -163, -2347 | C5 |
149379931009 | 523^2 * 739^2 | -523, -739 | C5 x C5 |
151851281761 | 347^2 * 1123^2 | -347, -1123 | C5 x C5 |
152975636641 | 227^2 * 1723^2 | -227, -1723 | C5 x C5 |
155501669569 | 179^2 * 2203^2 | -179, -2203 | C5 x C5 |
155678382721 | 571^2 * 691^2 | -571, -691 | C5 x C5 |
157266971761 | 227^2 * 1747^2 | -227, -1747 | C5 x C5 |
168915246049 | 11^2 * 37363^2 | -11, -37363 | C5 x C5 |
169415383201 | 523^2 * 787^2 | -523, -787 | C5 x C5 |
175997869441 | 443^2 * 947^2 | -443, -947 | C5 x C5 |
176494932769 | 179^2 * 2347^2 | -179, -2347 | C5 x C5 |
178740391729 | 619^2 * 683^2 | -619, -683 | C5 x C5 |
179614068481 | 227^2 * 1867^2 | -227, -1867 | C5 x C5 |
182952097441 | 619^2 * 691^2 | -619, -691 | C5 x C5 |
191256654241 | 163^2 * 2683^2 | -163, -2683 | C5 |
201939688129 | 571^2 * 787^2 | -571, -787 | C5 x C5 |
209252268481 | 619^2 * 739^2 | -619, -739 | C5 x C5 x C5 |
216776841649 | 443^2 * 1051^2 | -443, -1051 | C5 x C5 |
230646786049 | 179^2 * 2683^2 | -179, -2683 | C5 x C5 |
237318045409 | 619^2 * 787^2 | -619, -787 | C5 x C5 |
245303268961 | 523^2 * 947^2 | -523, -947 | C5 x C5 |
247495305121 | 443^2 * 1123^2 | -443, -1123 | C5 x C5 |
250081006561 | 227^2 * 2203^2 | -227, -2203 | C5 x C5 |
254759439169 | 683^2 * 739^2 | -683, -739 | C5 x C5 |
283842807361 | 227^2 * 2347^2 | -227, -2347 | C5 x C5 |
295736929489 | 691^2 * 787^2 | -691, -787 | C5 x C5 |
338250417649 | 739^2 * 787^2 | -739, -787 | C5 x C5 |
342455528809 | 47^2 * 12451^2 | -47, -12451 | C5 x C5 x C5 |
343622233249 | 619^2 * 947^2 | -619, -947 | C5 x C5 |
344955354241 | 523^2 * 1123^2 | -523, -1123 | C5 x C5 |
357461690161 | 347^2 * 1723^2 | -347, -1723 | C5 x C5 |
360145214641 | 571^2 * 1051^2 | -571, -1051 | C5 x C5 |
367489351681 | 347^2 * 1747^2 | -347, -1747 | C5 x C5 |
411179760289 | 571^2 * 1123^2 | -571, -1123 | C5 x C5 |
418351533601 | 683^2 * 947^2 | -683, -947 | C5 x C5 |
419708326801 | 347^2 * 1867^2 | -347, -1867 | C5 x C5 |
423240023761 | 619^2 * 1051^2 | -619, -1051 | C5 x C5 |
428209258129 | 691^2 * 947^2 | -691, -947 | C5 x C5 |
489766227889 | 739^2 * 947^2 | -739, -947 | C5 x C5 |
515284215889 | 683^2 * 1051^2 | -683, -1051 | C5 x C5 |
527425990081 | 691^2 * 1051^2 | -691, -1051 | C5 x C5 |
582610097521 | 443^2 * 1723^2 | -443, -1723 | C5 x C5 |
584370042481 | 347^2 * 2203^2 | -347, -2203 | C5 x C5 |
588302806081 | 683^2 * 1123^2 | -683, -1123 | C5 x C5 |
603245802721 | 739^2 * 1051^2 | -739, -1051 | C5 x C5 |
684062980561 | 443^2 * 1867^2 | -443, -1867 | C5 x C5 |
684155616769 | 787^2 * 1051^2 | -787, -1051 | C5 x C5 |
781104207601 | 787^2 * 1123^2 | -787, -1123 | C5 x C5 |
812033474641 | 523^2 * 1723^2 | -523, -1723 | C5 x C5 |
834812969761 | 523^2 * 1747^2 | -523, -1747 | C5 x C5 |
866762862001 | 347^2 * 2683^2 | -347, -2683 | C5 x C5 |
952437413041 | 443^2 * 2203^2 | -443, -2203 | C5 x C5 |
953437026481 | 523^2 * 1867^2 | -523, -1867 | C5 x C5 |
967526009641 | 79^2 * 12451^2 | -79, -12451 | C5 x C5 x C5 |
967927371889 | 571^2 * 1723^2 | -571, -1723 | C5 x C5 |
995080066369 | 571^2 * 1747^2 | -571, -1747 | C5 x C5 |
1081019757841 | 443^2 * 2347^2 | -443, -2347 | C5 x C5 |
1130991837361 | 947^2 * 1123^2 | -947, -1123 | C5 x C5 |
1136477527249 | 571^2 * 1867^2 | -571, -1867 | C5 x C5 |
1137501172369 | 619^2 * 1723^2 | -619, -1723 | C5 x C5 |
1169410820449 | 619^2 * 1747^2 | -619, -1747 | C5 x C5 |
1327493404561 | 523^2 * 2203^2 | -523, -2203 | C5 x C5 |
1393044354529 | 1051^2 * 1123^2 | -1051, -1123 | C5 x C5 |
1417511691649 | 691^2 * 1723^2 | -691, -1723 | C5 x C5 |
1423728626401 | 683^2 * 1747^2 | -683, -1747 | C5 x C5 |
1457276309329 | 691^2 * 1747^2 | -691, -1747 | C5 x C5 |
1506709605361 | 523^2 * 2347^2 | -523, -2347 | C5 x C5 |
1582345115569 | 571^2 * 2203^2 | -571, -2203 | C5 x C5 |
1621285250209 | 739^2 * 1723^2 | -739, -1723 | C5 x C5 |
1626035575921 | 683^2 * 1867^2 | -683, -1867 | C5 x C5 |
1644685697209 | 103^2 * 12451^2 | -103, -12451 | C5 x C5 x C5 |
1664350269409 | 691^2 * 1867^2 | -691, -1867 | C5 x C5 |
1666766207089 | 739^2 * 1747^2 | -739, -1747 | C5 x C5 |
1795967178769 | 571^2 * 2347^2 | -571, -2347 | C5 x C5 |
1890319762321 | 787^2 * 1747^2 | -787, -1747 | C5 x C5 |
1903607962369 | 739^2 * 1867^2 | -739, -1867 | C5 x C5 |
1968995497681 | 523^2 * 2683^2 | -523, -2683 | C5 x C5 |
2110607500849 | 619^2 * 2347^2 | -619, -2347 | C5 x C5 |
2263968613201 | 683^2 * 2203^2 | -683, -2203 | C5 x C5 |
2317315086529 | 691^2 * 2203^2 | -691, -2203 | C5 x C5 |
2347002552049 | 571^2 * 2683^2 | -571, -2683 | C5 x C5 |
2569612206001 | 683^2 * 2347^2 | -683, -2347 | C5 x C5 |
2581192478881 | 43^2 * 37363^2 | -43, -37363 | C5 x C5 |
2650439352289 | 739^2 * 2203^2 | -739, -2203 | C5 x C5 |
2660425228561 | 131^2 * 12451^2 | -131, -12451 | C5 x C5 x C5 |
2662382885761 | 947^2 * 1723^2 | -947, -1723 | C5 x C5 |
2737069139281 | 947^2 * 1747^2 | -947, -1747 | C5 x C5 |
2758180243729 | 619^2 * 2683^2 | -619, -2683 | C5 x C5 |
3005927205121 | 787^2 * 2203^2 | -787, -2203 | C5 x C5 x C5 |
3008257831489 | 739^2 * 2347^2 | -739, -2347 | C5 x C5 |
3083750235721 | 47^2 * 37363^2 | -47, -37363 | C5 x C5 x C5 |
3279261022129 | 1051^2 * 1723^2 | -1051, -1723 | C5 x C5 |
3358015935121 | 683^2 * 2683^2 | -683, -2683 | C5 x C5 |
3371252193409 | 1051^2 * 1747^2 | -1051, -1747 | C5 x C5 |
3411737773921 | 787^2 * 2347^2 | -787, -2347 | C5 x C5 |
3437141726209 | 691^2 * 2683^2 | -691, -2683 | C5 x C5 |
3743950235041 | 1123^2 * 1723^2 | -1123, -1723 | C5 x C5 |
3931246011169 | 739^2 * 2683^2 | -739, -2683 | C5 x C5 |
4118923017169 | 163^2 * 12451^2 | -163, -12451 | C5 x C5 |
4352401510081 | 947^2 * 2203^2 | -947, -2203 | C5 x C5 |
4395903482881 | 1123^2 * 1867^2 | -1123, -1867 | C5 x C5 |
4458520933441 | 787^2 * 2683^2 | -787, -2683 | C5 x C5 |
4939990766881 | 947^2 * 2347^2 | -947, -2347 | C5 x C5 |
4967232955441 | 179^2 * 12451^2 | -179, -12451 | C5 x C5 x C5 |
5360859514609 | 1051^2 * 2203^2 | -1051, -2203 | C5 x C5 |
6084594089809 | 1051^2 * 2347^2 | -1051, -2347 | C5 x C5 |
6266616029041 | 67^2 * 37363^2 | -67, -37363 | C5 x C5 |
6946814333761 | 1123^2 * 2347^2 | -1123, -2347 | C5 x C5 |
7951458147889 | 1051^2 * 2683^2 | -1051, -2683 | C5 x C5 |
8712397112329 | 79^2 * 37363^2 | -79, -37363 | C5 x C5 x C5 |
9060587626561 | 1723^2 * 1747^2 | -1723, -1747 | C5 x C5 |
9078223234081 | 1123^2 * 2683^2 | -1123, -2683 | C5 x C5 |
10348066019281 | 1723^2 * 1867^2 | -1723, -1867 | C5 x C5 |
10638354199201 | 1747^2 * 1867^2 | -1747, -1867 | C5 x C5 |
14407862301361 | 1723^2 * 2203^2 | -1723, -2203 | C5 x C5 |
14810097895321 | 103^2 * 37363^2 | -103, -37363 | C5 x C5 x C5 |
16352973542161 | 1723^2 * 2347^2 | -1723, -2347 | C5 x C5 |
16811713843681 | 1747^2 * 2347^2 | -1747, -2347 | C5 x C5 |
16916777226001 | 1867^2 * 2203^2 | -1867, -2203 | C5 x C5 |
18666694327009 | 347^2 * 12451^2 | -347, -12451 | C5 x C5 x C5 |
19200600658801 | 1867^2 * 2347^2 | -1867, -2347 | C5 x C5 |
21370363050481 | 1723^2 * 2683^2 | -1723, -2683 | C5 x C5 |
21969853214401 | 1747^2 * 2683^2 | -1747, -2683 | C5 x C5 |
22515983500201 | 127^2 * 37363^2 | -127, -37363 | C5 x C5 x C5 |
23956649069809 | 131^2 * 37363^2 | -131, -37363 | C5 x C5 x C5 |
25091693923921 | 1867^2 * 2683^2 | -1867, -2683 | C5 x C5 |
26733460134481 | 2203^2 * 2347^2 | -2203, -2347 | C5 x C5 |
30423972418849 | 443^2 * 12451^2 | -443, -12451 | C5 x C5 x C5 |
34935771601201 | 2203^2 * 2683^2 | -2203, -2683 | C5 x C5 |
37090158448561 | 163^2 * 37363^2 | -163, -37363 | C5 x C5 |
39652221594001 | 2347^2 * 2683^2 | -2347, -2683 | C5 x C5 |
42404489968129 | 523^2 * 12451^2 | -523, -12451 | C5 x C5 x C5 |
44729036352529 | 179^2 * 37363^2 | -179, -37363 | C5 x C5 x C5 |
50545288849441 | 571^2 * 12451^2 | -571, -12451 | C5 x C5 x C5 |
59400453994561 | 619^2 * 12451^2 | -619, -12451 | C5 x C5 x C5 |
72318577265089 | 683^2 * 12451^2 | -683, -12451 | C5 x C5 x C5 |
74022638456881 | 691^2 * 12451^2 | -691, -12451 | C5 x C5 x C5 |
96019166329969 | 787^2 * 12451^2 | -787, -12451 | C5 x C5 x C5 |
139029968463409 | 947^2 * 12451^2 | -947, -12451 | C5 x C5 x C5 |
168090213731521 | 347^2 * 37363^2 | -347, -37363 | C5 x C5 x C5 |
171243422172001 | 1051^2 * 12451^2 | -1051, -12451 | C5 x C5 x C5 |
195509551195729 | 1123^2 * 12451^2 | -1123, -12451 | C5 x C5 x C5 |
273962381172481 | 443^2 * 37363^2 | -443, -37363 | C5 x C5 x C5 |
381844779640801 | 523^2 * 37363^2 | -523, -37363 | C5 x C5 x C5 |
455151204438529 | 571^2 * 37363^2 | -571, -37363 | C5 x C5 x C5 |
460234341143329 | 1723^2 * 12451^2 | -1723, -12451 | C5 x C5 x C5 |
473145023098609 | 1747^2 * 12451^2 | -1747, -12451 | C5 x C5 x C5 |
534890368523809 | 619^2 * 37363^2 | -619, -37363 | C5 x C5 x C5 |
540377306364289 | 1867^2 * 12451^2 | -1867, -12451 | C5 x C5 x C5 |
752380377779809 | 2203^2 * 12451^2 | -2203, -12451 | C5 x C5 x C5 |
762381513120049 | 739^2 * 37363^2 | -739, -37363 | C5 x C5 x C5 |
853954330915009 | 2347^2 * 12451^2 | -2347, -12451 | C5 x C5 x C5 |
864635264711761 | 787^2 * 37363^2 | -787, -37363 | C5 x C5 x C5 |
1115963040797089 | 2683^2 * 12451^2 | -2683, -12451 | C5 x C5 x C5 |
1542016113231169 | 1051^2 * 37363^2 | -1051, -37363 | C5 x C5 x C5 |
1760528225905201 | 1123^2 * 37363^2 | -1123, -37363 | C5 x C5 x C5 |
4144327185849601 | 1723^2 * 37363^2 | -1723, -37363 | C5 x C5 x C5 |
6775049523654721 | 2203^2 * 37363^2 | -2203, -37363 | C5 x C5 x C5 |
7689704641103521 | 2347^2 * 37363^2 | -2347, -37363 | C5 x C5 x C5 |
10049045790215041 | 2683^2 * 37363^2 | -2683, -37363 | C5 x C5 x C5 |
216417285820264369 | 12451^2 * 37363^2 | -12451, -37363 | C5 x C5 x C5 x C5 |
Die folgende Tabelle enthält alle imaginären biquadratischen Körper der Familie 2b mit Exponent 5. Die Ergebnisse werden unter Verwendung von ERH für imaginärquadratische Zahlenkörper bewiesen.
Diskriminante | Faktorisierung | Erzeuger | Klassengruppe |
14161 | 7^2 * 17^2 | -7, 17 | C5 |
20449 | 11^2 * 13^2 | -11, 13 | C5 |
25281 | 3^2 * 53^2 | -3, 53 | C5 |
55225 | 5^2 * 47^2 | -47, 5 | C5 |
87616 | 2^6 * 37^2 | -8, 37 | C5 |
91809 | 3^2 * 101^2 | -3, 101 | C5 |
101761 | 11^2 * 29^2 | -11, 29 | C5 |
118336 | 2^6 * 43^2 | -43, 8 | C5 |
238144 | 2^6 * 61^2 | -8, 61 | C5 |
373321 | 13^2 * 47^2 | -47, 13 | C5 x C5 |
403225 | 5^2 * 127^2 | -127, 5 | C5 x C5 |
488601 | 3^2 * 233^2 | -3, 233 | C5 |
524176 | 2^4 * 181^2 | -4, 181 | C5 |
606841 | 19^2 * 41^2 | -19, 41 | C5 |
620944 | 2^4 * 197^2 | -4, 197 | C5 |
644809 | 11^2 * 73^2 | -11, 73 | C5 |
760384 | 2^6 * 109^2 | -8, 109 | C5 |
1607824 | 2^4 * 317^2 | -4, 317 | C5 |
1915456 | 2^6 * 173^2 | -8, 173 | C5 |
2226064 | 2^4 * 373^2 | -4, 373 | C5 |
2483776 | 2^6 * 197^2 | -8, 197 | C5 |
2835856 | 2^4 * 421^2 | -4, 421 | C5 |
2913849 | 3^2 * 569^2 | -3, 569 | C5 |
3164841 | 3^2 * 593^2 | -3, 593 | C5 |
3697929 | 3^2 * 641^2 | -3, 641 | C5 |
4631104 | 2^6 * 269^2 | -8, 269 | C5 |
4682896 | 2^4 * 541^2 | -4, 541 | C5 |
6012304 | 2^4 * 613^2 | -4, 613 | C5 |
6985449 | 3^2 * 881^2 | -3, 881 | C5 |
7706176 | 2^6 * 347^2 | -347, 8 | C5 x C5 |
8042896 | 2^4 * 709^2 | -4, 709 | C5 |
9168784 | 2^4 * 757^2 | -4, 757 | C5 |
9554281 | 11^2 * 281^2 | -11, 281 | C5 |
9853321 | 43^2 * 73^2 | -43, 73 | C5 |
9903609 | 3^2 * 1049^2 | -3, 1049 | C5 |
10830681 | 3^2 * 1097^2 | -3, 1097 | C5 |
11641744 | 2^4 * 853^2 | -4, 853 | C5 |
12306064 | 2^4 * 877^2 | -4, 877 | C5 |
13446889 | 19^2 * 193^2 | -19, 193 | C5 |
13564489 | 29^2 * 127^2 | -127, 29 | C5 x C5 |
14523721 | 37^2 * 103^2 | -103, 37 | C5 x C5 |
14891881 | 17^2 * 227^2 | -227, 17 | C5 x C5 |
16670889 | 3^2 * 1361^2 | -3, 1361 | C5 |
17867529 | 3^2 * 1409^2 | -3, 1409 | C5 |
19114384 | 2^4 * 1093^2 | -4, 1093 | C5 x C5 |
20967241 | 19^2 * 241^2 | -19, 241 | C5 |
21409129 | 7^2 * 661^2 | -7, 661 | C5 |
23541904 | 2^4 * 1213^2 | -4, 1213 | C5 |
26656569 | 3^2 * 1721^2 | -3, 1721 | C5 |
32114889 | 3^2 * 1889^2 | -3, 1889 | C5 |
33674809 | 7^2 * 829^2 | -7, 829 | C5 |
39175081 | 11^2 * 569^2 | -11, 569 | C5 |
40998409 | 19^2 * 337^2 | -19, 337 | C5 |
55995289 | 7^2 * 1069^2 | -7, 1069 | C5 |
67683529 | 19^2 * 433^2 | -19, 433 | C5 |
86620249 | 41^2 * 227^2 | -227, 41 | C5 x C5 |
109893289 | 11^2 * 953^2 | -11, 953 | C5 |
191628649 | 109^2 * 127^2 | -127, 109 | C5 x C5 |
1124327961 | 3^2 * 11177^2 | -3, 11177 | C5 x C5 |
1595762809 | 43^2 * 929^2 | -43, 929 | C5 x C5 |
3922767424 | 2^6 * 7829^2 | -8, 7829 | C5 x C5 |
4873575721 | 7^2 * 9973^2 | -7, 9973 | C5 x C5 |
5728673344 | 2^6 * 9461^2 | -8, 9461 | C5 x C5 |
7241839801 | 7^2 * 12157^2 | -7, 12157 | C5 x C5 |
13499418969 | 3^2 * 38729^2 | -3, 38729 | C5 x C5 |
22990747129 | 7^2 * 21661^2 | -7, 21661 | C5 x C5 |
23841830464 | 2^6 * 19301^2 | -8, 19301 | C5 x C5 |
C-Programme
Die folgenden zwei C-Programme können verwendet werden, um alle imaginärquadratischen Zahlkörper mit einem Exponenten kleiner oder gleich 8 und einer Diskriminantenschranke von 3.1·1020 zu berechnen.
Julia Programme
Die folgende Datei enthält den Julia-Code. Sie müssen Julia einschließlich des Hecke- und des Markdown-Pakets installieren. Die Funktion M1 berechnet die imaginärquadratischen Zahlkörper eines gegebenen Exponenten. Die Funktionen M2a, M2b, M3a und M3b berechnen die entsprechenden Familien.
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