Imaginärquadratische Zahlkörper mit kleinem Exponenten

Hier sind Listen mit imaginärquadratischen Körpern mit Klassengruppenexponent bis 8. Für Exponent 1 ist die Liste vollständig. Für die Exponenten 2,4,8 sind die Listen vollständig, vorausgesetzt, es gibt keine Siegel-Nullstellen. Ohne diese Annahme könnte ein Körper fehlen. Für die Exponenten 3 und 5 sind die Listen unter der Annahme der verallgemeinerten Riemann-Vermutung vollständig. Ohne diese Annahme ist bekannt, dass es endlich viele Körper mit Exponent 3 oder 5 gibt. Für Exponent 6 ist die Liste bis zur Diskriminante 3.1·10^20. vollständig. Es ist bekannt, dass es mit Exponent 6 endlich viele Körper gibt. Für Exponent 7 ist die Liste bis zur Diskriminante 3.1·10^20. vollständig. Es ist nicht bekannt, ob es nur endlich viele Körper mit Exponent 7 gibt. Unter der Annahme der verallgemeinerten Riemann-Vermutung konergiert der Exponent nach unendlich, daher gibt es dann nur endlich viele Körper mit gegebenem Exponenten.

Der wissenschaftliche Inhalt steht in der Arbeit:

A.-S. Elsenhans, J. Klüners, F. Nicolae, Imaginary quadratic number fields with class groups of small exponent , Acta Arith., 193, 2020, 217-233.

Liste von 9 Körpern mit Exponent 1

Die folgende Tabelle enthält alle Körper mit Exponent 1.

Diskriminante	Faktorisierung	Klassengruppe
-3	-3	C1
-4	-2^2	C1
-7	-7	C1
-8	-2^3	C1
-11	-11	C1
-19	-19	C1
-43	-43	C1
-67	-67	C1
-163	-163	C1

Liste von 56 Körpern mit Exponent 2

Die folgende Tabelle ist vollständig, sofern es keine Siegel-Nullstellen gibt. Ohne Annahme einer Vermutung könnte ein Körper fehlen.

Diskriminante	Faktorisierung	Klassengruppe
-15	-3 * 5	C2
-20	-2^2 * 5	C2
-24	-2^3 * 3	C2
-35	-5 * 7	C2
-40	-2^3 * 5	C2
-51	-3 * 17	C2
-52	-2^2 * 13	C2
-84	-2^2 * 3 * 7	C2 x C2
-88	-2^3 * 11	C2
-91	-7 * 13	C2
-115	-5 * 23	C2
-120	-2^3 * 3 * 5	C2 x C2
-123	-3 * 41	C2
-132	-2^2 * 3 * 11	C2 x C2
-148	-2^2 * 37	C2
-168	-2^3 * 3 * 7	C2 x C2
-187	-11 * 17	C2
-195	-3 * 5 * 13	C2 x C2
-228	-2^2 * 3 * 19	C2 x C2
-232	-2^3 * 29	C2
-235	-5 * 47	C2
-267	-3 * 89	C2
-280	-2^3 * 5 * 7	C2 x C2
-312	-2^3 * 3 * 13	C2 x C2
-340	-2^2 * 5 * 17	C2 x C2
-372	-2^2 * 3 * 31	C2 x C2
-403	-13 * 31	C2
-408	-2^3 * 3 * 17	C2 x C2
-420	-2^2 * 3 * 5 * 7	C2 x C2 x C2
-427	-7 * 61	C2
-435	-3 * 5 * 29	C2 x C2
-483	-3 * 7 * 23	C2 x C2
-520	-2^3 * 5 * 13	C2 x C2
-532	-2^2 * 7 * 19	C2 x C2
-555	-3 * 5 * 37	C2 x C2
-595	-5 * 7 * 17	C2 x C2
-627	-3 * 11 * 19	C2 x C2
-660	-2^2 * 3 * 5 * 11	C2 x C2 x C2
-708	-2^2 * 3 * 59	C2 x C2
-715	-5 * 11 * 13	C2 x C2
-760	-2^3 * 5 * 19	C2 x C2
-795	-3 * 5 * 53	C2 x C2
-840	-2^3 * 3 * 5 * 7	C2 x C2 x C2
-1012	-2^2 * 11 * 23	C2 x C2
-1092	-2^2 * 3 * 7 * 13	C2 x C2 x C2
-1155	-3 * 5 * 7 * 11	C2 x C2 x C2
-1320	-2^3 * 3 * 5 * 11	C2 x C2 x C2
-1380	-2^2 * 3 * 5 * 23	C2 x C2 x C2
-1428	-2^2 * 3 * 7 * 17	C2 x C2 x C2
-1435	-5 * 7 * 41	C2 x C2
-1540	-2^2 * 5 * 7 * 11	C2 x C2 x C2
-1848	-2^3 * 3 * 7 * 11	C2 x C2 x C2
-1995	-3 * 5 * 7 * 19	C2 x C2 x C2
-3003	-3 * 7 * 11 * 13	C2 x C2 x C2
-3315	-3 * 5 * 13 * 17	C2 x C2 x C2
-5460	-2^2 * 3 * 5 * 7 * 13	C2 x C2 x C2 x C2

Liste von 17 Körpern mit Exponent 3

Die folgende Tabelle ist vollständig unter der Annahme, dass die verallgemeinerte Riemann-Vermutung wahr ist. Ohne Vermutung ist bekannt, dass die Liste endlich ist.

Diskriminante	Faktorisierung	Klassengruppe
-23	-23	C3
-31	-31	C3
-59	-59	C3
-83	-83	C3
-107	-107	C3
-139	-139	C3
-211	-211	C3
-283	-283	C3
-307	-307	C3
-331	-331	C3
-379	-379	C3
-499	-499	C3
-547	-547	C3
-643	-643	C3
-883	-883	C3
-907	-907	C3
-4027	-4027	C3 x C3

Liste von 203 Körpern mit Exponent 4

Die folgende Tabelle ist vollständig, sofern keine Siegel-Nullstellen gibt. Ohne Annahme einer Vermutung könnte ein Köper fehlen.

Diskriminante	Faktorisierung	Klassengruppe
-39	-3 * 13	C4
-55	-5 * 11	C4
-56	-2^3 * 7	C4
-68	-2^2 * 17	C4
-136	-2^3 * 17	C4
-155	-5 * 31	C4
-184	-2^3 * 23	C4
-203	-7 * 29	C4
-219	-3 * 73	C4
-259	-7 * 37	C4
-260	-2^2 * 5 * 13	C2 x C4
-264	-2^3 * 3 * 11	C2 x C4
-276	-2^2 * 3 * 23	C2 x C4
-291	-3 * 97	C4
-292	-2^2 * 73	C4
-308	-2^2 * 7 * 11	C2 x C4
-323	-17 * 19	C4
-328	-2^3 * 41	C4
-355	-5 * 71	C4
-388	-2^2 * 97	C4
-456	-2^3 * 3 * 19	C2 x C4
-552	-2^3 * 3 * 23	C2 x C4
-564	-2^2 * 3 * 47	C2 x C4
-568	-2^3 * 71	C4
-580	-2^2 * 5 * 29	C2 x C4
-616	-2^3 * 7 * 11	C2 x C4
-651	-3 * 7 * 31	C2 x C4
-667	-23 * 29	C4
-723	-3 * 241	C4
-763	-7 * 109	C4
-772	-2^2 * 193	C4
-820	-2^2 * 5 * 41	C2 x C4
-852	-2^2 * 3 * 71	C2 x C4
-868	-2^2 * 7 * 31	C2 x C4
-915	-3 * 5 * 61	C2 x C4
-952	-2^3 * 7 * 17	C2 x C4
-955	-5 * 191	C4
-987	-3 * 7 * 47	C2 x C4
-1003	-17 * 59	C4
-1027	-13 * 79	C4
-1032	-2^3 * 3 * 43	C2 x C4
-1060	-2^2 * 5 * 53	C2 x C4
-1128	-2^3 * 3 * 47	C2 x C4
-1131	-3 * 13 * 29	C2 x C4
-1140	-2^2 * 3 * 5 * 19	C2 x C2 x C4
-1204	-2^2 * 7 * 43	C2 x C4
-1227	-3 * 409	C4
-1240	-2^3 * 5 * 31	C2 x C4
-1243	-11 * 113	C4
-1288	-2^3 * 7 * 23	C2 x C4
-1387	-19 * 73	C4
-1411	-17 * 83	C4
-1443	-3 * 13 * 37	C2 x C4
-1507	-11 * 137	C4
-1555	-5 * 311	C4
-1560	-2^3 * 3 * 5 * 13	C2 x C2 x C4
-1635	-3 * 5 * 109	C2 x C4
-1659	-3 * 7 * 79	C2 x C4
-1672	-2^3 * 11 * 19	C2 x C4
-1716	-2^2 * 3 * 11 * 13	C2 x C2 x C4
-1752	-2^3 * 3 * 73	C2 x C4
-1768	-2^3 * 13 * 17	C2 x C4
-1771	-7 * 11 * 23	C2 x C4
-1780	-2^2 * 5 * 89	C2 x C4
-1860	-2^2 * 3 * 5 * 31	C2 x C2 x C4
-1947	-3 * 11 * 59	C2 x C4
-1992	-2^3 * 3 * 83	C2 x C4
-2020	-2^2 * 5 * 101	C2 x C4
-2035	-5 * 11 * 37	C2 x C4
-2040	-2^3 * 3 * 5 * 17	C2 x C2 x C4
-2067	-3 * 13 * 53	C2 x C4
-2139	-3 * 23 * 31	C2 x C4
-2163	-3 * 7 * 103	C2 x C4
-2212	-2^2 * 7 * 79	C2 x C4
-2244	-2^2 * 3 * 11 * 17	C2 x C2 x C4
-2280	-2^3 * 3 * 5 * 19	C2 x C2 x C4
-2379	-3 * 13 * 61	C4 x C4
-2392	-2^3 * 13 * 23	C2 x C4
-2436	-2^2 * 3 * 7 * 29	C2 x C2 x C4
-2451	-3 * 19 * 43	C2 x C4
-2580	-2^2 * 3 * 5 * 43	C2 x C2 x C4
-2632	-2^3 * 7 * 47	C2 x C4
-2667	-3 * 7 * 127	C2 x C4
-2715	-3 * 5 * 181	C2 x C4
-2755	-5 * 19 * 29	C2 x C4
-2760	-2^3 * 3 * 5 * 23	C2 x C2 x C4
-2788	-2^2 * 17 * 41	C2 x C4
-2968	-2^3 * 7 * 53	C2 x C4
-3108	-2^2 * 3 * 7 * 37	C2 x C2 x C4
-3172	-2^2 * 13 * 61	C2 x C4
-3192	-2^3 * 3 * 7 * 19	C2 x C2 x C4
-3220	-2^2 * 5 * 7 * 23	C2 x C2 x C4
-3243	-3 * 23 * 47	C2 x C4
-3355	-5 * 11 * 61	C2 x C4
-3432	-2^3 * 3 * 11 * 13	C2 x C2 x C4
-3480	-2^3 * 3 * 5 * 29	C2 x C2 x C4
-3507	-3 * 7 * 167	C2 x C4
-3588	-2^2 * 3 * 13 * 23	C2 x C2 x C4
-3640	-2^3 * 5 * 7 * 13	C2 x C2 x C4
-3795	-3 * 5 * 11 * 23	C2 x C2 x C4
-3828	-2^2 * 3 * 11 * 29	C2 x C2 x C4
-4020	-2^2 * 3 * 5 * 67	C2 x C2 x C4
-4123	-7 * 19 * 31	C2 x C4
-4180	-2^2 * 5 * 11 * 19	C2 x C2 x C4
-4260	-2^2 * 3 * 5 * 71	C2 x C2 x C4
-4323	-3 * 11 * 131	C2 x C4
-4420	-2^2 * 5 * 13 * 17	C2 x C2 x C4
-4440	-2^3 * 3 * 5 * 37	C2 x C2 x C4
-4452	-2^2 * 3 * 7 * 53	C2 x C2 x C4
-4488	-2^3 * 3 * 11 * 17	C2 x C2 x C4
-4515	-3 * 5 * 7 * 43	C2 x C2 x C4
-4740	-2^2 * 3 * 5 * 79	C2 x C2 x C4
-5083	-13 * 17 * 23	C2 x C4
-5115	-3 * 5 * 11 * 31	C2 x C2 x C4
-5160	-2^3 * 3 * 5 * 43	C2 x C2 x C4
-5187	-3 * 7 * 13 * 19	C2 x C2 x C4
-5208	-2^3 * 3 * 7 * 31	C2 x C2 x C4
-5412	-2^2 * 3 * 11 * 41	C2 x C2 x C4
-5467	-7 * 11 * 71	C2 x C4
-6052	-2^2 * 17 * 89	C4 x C4
-6123	-3 * 13 * 157	C4 x C4
-6195	-3 * 5 * 7 * 59	C2 x C2 x C4
-6307	-7 * 17 * 53	C2 x C4
-6328	-2^3 * 7 * 113	C4 x C4
-6355	-5 * 31 * 41	C4 x C4
-6360	-2^3 * 3 * 5 * 53	C2 x C4 x C4
-6420	-2^2 * 3 * 5 * 107	C2 x C2 x C4
-6580	-2^2 * 5 * 7 * 47	C2 x C2 x C4
-6612	-2^2 * 3 * 19 * 29	C2 x C2 x C4
-6708	-2^2 * 3 * 13 * 43	C2 x C2 x C4
-6820	-2^2 * 5 * 11 * 31	C2 x C2 x C4
-7035	-3 * 5 * 7 * 67	C2 x C2 x C4
-7140	-2^2 * 3 * 5 * 7 * 17	C2 x C2 x C2 x C4
-7315	-5 * 7 * 11 * 19	C2 x C2 x C4
-7395	-3 * 5 * 17 * 29	C2 x C2 x C4
-7480	-2^3 * 5 * 11 * 17	C2 x C2 x C4
-7540	-2^2 * 5 * 13 * 29	C2 x C2 x C4
-7672	-2^3 * 7 * 137	C4 x C4
-7755	-3 * 5 * 11 * 47	C2 x C2 x C4
-7995	-3 * 5 * 13 * 41	C2 x C2 x C4
-8008	-2^3 * 7 * 11 * 13	C2 x C2 x C4
-8052	-2^2 * 3 * 11 * 61	C2 x C2 x C4
-8547	-3 * 7 * 11 * 37	C2 x C2 x C4
-8580	-2^2 * 3 * 5 * 11 * 13	C2 x C2 x C2 x C4
-8680	-2^3 * 5 * 7 * 31	C2 x C2 x C4
-8715	-3 * 5 * 7 * 83	C2 x C2 x C4
-8835	-3 * 5 * 19 * 31	C2 x C2 x C4
-8932	-2^2 * 7 * 11 * 29	C2 x C2 x C4
-9240	-2^3 * 3 * 5 * 7 * 11	C2 x C2 x C2 x C4
-9595	-5 * 19 * 101	C4 x C4
-9867	-3 * 11 * 13 * 23	C2 x C2 x C4
-9955	-5 * 11 * 181	C4 x C4
-10168	-2^3 * 31 * 41	C4 x C4
-10803	-3 * 13 * 277	C4 x C4
-10920	-2^3 * 3 * 5 * 7 * 13	C2 x C2 x C2 x C4
-10948	-2^2 * 7 * 17 * 23	C2 x C2 x C4
-11067	-3 * 7 * 17 * 31	C2 x C2 x C4
-11715	-3 * 5 * 11 * 71	C2 x C2 x C4
-12180	-2^2 * 3 * 5 * 7 * 29	C2 x C2 x C2 x C4
-12595	-5 * 11 * 229	C4 x C4
-13195	-5 * 7 * 13 * 29	C2 x C2 x C4
-14008	-2^3 * 17 * 103	C4 x C4
-14155	-5 * 19 * 149	C4 x C4
-14280	-2^3 * 3 * 5 * 7 * 17	C2 x C2 x C2 x C4
-14547	-3 * 13 * 373	C4 x C4
-14763	-3 * 7 * 19 * 37	C2 x C2 x C4
-14820	-2^2 * 3 * 5 * 13 * 19	C2 x C2 x C2 x C4
-16555	-5 * 7 * 11 * 43	C2 x C2 x C4
-17220	-2^2 * 3 * 5 * 7 * 41	C2 x C2 x C2 x C4
-17427	-3 * 37 * 157	C4 x C4
-19240	-2^3 * 5 * 13 * 37	C2 x C4 x C4
-19320	-2^3 * 3 * 5 * 7 * 23	C2 x C2 x C2 x C4
-19380	-2^2 * 3 * 5 * 17 * 19	C2 x C2 x C2 x C4
-19635	-3 * 5 * 7 * 11 * 17	C2 x C2 x C2 x C4
-19947	-3 * 61 * 109	C4 x C4
-20020	-2^2 * 5 * 7 * 11 * 13	C2 x C2 x C2 x C4
-20148	-2^2 * 3 * 23 * 73	C2 x C4 x C4
-20155	-5 * 29 * 139	C4 x C4
-23640	-2^3 * 3 * 5 * 197	C2 x C4 x C4
-25608	-2^3 * 3 * 11 * 97	C2 x C4 x C4
-30340	-2^2 * 5 * 37 * 41	C2 x C4 x C4
-31395	-3 * 5 * 7 * 13 * 23	C2 x C2 x C2 x C4
-33915	-3 * 5 * 7 * 17 * 19	C2 x C2 x C2 x C4
-34840	-2^3 * 5 * 13 * 67	C2 x C4 x C4
-40755	-3 * 5 * 11 * 13 * 19	C2 x C2 x C2 x C4
-42420	-2^2 * 3 * 5 * 7 * 101	C2 x C2 x C4 x C4
-43435	-5 * 7 * 17 * 73	C2 x C4 x C4
-44115	-3 * 5 * 17 * 173	C2 x C4 x C4
-46852	-2^2 * 13 * 17 * 53	C2 x C4 x C4
-53592	-2^3 * 3 * 7 * 11 * 29	C2 x C2 x C4 x C4
-57387	-3 * 11 * 37 * 47	C2 x C4 x C4
-57715	-5 * 7 * 17 * 97	C2 x C4 x C4
-58548	-2^2 * 3 * 7 * 17 * 41	C2 x C2 x C4 x C4
-73140	-2^2 * 3 * 5 * 23 * 53	C2 x C2 x C4 x C4
-82555	-5 * 11 * 19 * 79	C2 x C4 x C4
-92568	-2^3 * 3 * 7 * 19 * 29	C2 x C2 x C4 x C4
-105315	-3 * 5 * 7 * 17 * 59	C2 x C2 x C4 x C4
-111435	-3 * 5 * 17 * 19 * 23	C2 x C2 x C4 x C4
-198660	-2^2 * 3 * 5 * 7 * 11 * 43	C2 x C2 x C2 x C4 x C4
-207480	-2^3 * 3 * 5 * 7 * 13 * 19	C2 x C2 x C2 x C4 x C4
-228228	-2^2 * 3 * 7 * 11 * 13 * 19	C2 x C2 x C2 x C4 x C4
-264180	-2^2 * 3 * 5 * 7 * 17 * 37	C2 x C2 x C2 x C4 x C4
-435435	-3 * 5 * 7 * 11 * 13 * 29	C2 x C2 x C2 x C4 x C4

Liste von 27 Körpern mit Exponent 5

Die folgende Tabelle ist vollständig unter der Annahme, dass die verallgemeinerte Riemann-Vermutung wahr ist. Ohne Annahme einer Vermutung ist bekannt, dass die Liste endlich ist.

Diskriminante	Faktorisierung	Klassengruppe
-47	-47	C5
-79	-79	C5
-103	-103	C5
-127	-127	C5
-131	-131	C5
-179	-179	C5
-227	-227	C5
-347	-347	C5
-443	-443	C5
-523	-523	C5
-571	-571	C5
-619	-619	C5
-683	-683	C5
-691	-691	C5
-739	-739	C5
-787	-787	C5
-947	-947	C5
-1051	-1051	C5
-1123	-1123	C5
-1723	-1723	C5
-1747	-1747	C5
-1867	-1867	C5
-2203	-2203	C5
-2347	-2347	C5
-2683	-2683	C5
-12451	-12451	C5 x C5
-37363	-37363	C5 x C5

Liste von 432 Feldern mit Exponent 6

Die folgende Tabelle ist nur bis zur Diskriminante 3.1 * 10 ^ 20 vollständig. Es ist bekannt, dass es nur eine endliche Anzahl von Körpern mit Exponent 6 gibt.

Diskriminante	Faktorisierung	Klassengruppe
-87	-3 * 29	C6
-104	-2^3 * 13	C6
-116	-2^2 * 29	C6
-152	-2^3 * 19	C6
-212	-2^2 * 53	C6
-231	-3 * 7 * 11	C2 x C6
-244	-2^2 * 61	C6
-247	-13 * 19	C6
-255	-3 * 5 * 17	C2 x C6
-339	-3 * 113	C6
-411	-3 * 137	C6
-424	-2^3 * 53	C6
-436	-2^2 * 109	C6
-440	-2^3 * 5 * 11	C2 x C6
-451	-11 * 41	C6
-472	-2^3 * 59	C6
-515	-5 * 103	C6
-516	-2^2 * 3 * 43	C2 x C6
-628	-2^2 * 157	C6
-680	-2^3 * 5 * 17	C2 x C6
-696	-2^3 * 3 * 29	C2 x C6
-707	-7 * 101	C6
-728	-2^3 * 7 * 13	C2 x C6
-744	-2^3 * 3 * 31	C2 x C6
-771	-3 * 257	C6
-804	-2^2 * 3 * 67	C2 x C6
-808	-2^3 * 101	C6
-835	-5 * 167	C6
-843	-3 * 281	C6
-856	-2^3 * 107	C6
-888	-2^3 * 3 * 37	C2 x C6
-948	-2^2 * 3 * 79	C2 x C6
-984	-2^3 * 3 * 41	C2 x C6
-996	-2^2 * 3 * 83	C2 x C6
-1048	-2^3 * 131	C6
-1059	-3 * 353	C6
-1099	-7 * 157	C6
-1108	-2^2 * 277	C6
-1144	-2^3 * 11 * 13	C2 x C6
-1147	-31 * 37	C6
-1192	-2^3 * 149	C6
-1203	-3 * 401	C6
-1219	-23 * 53	C6
-1235	-5 * 13 * 19	C2 x C6
-1236	-2^2 * 3 * 103	C2 x C6
-1267	-7 * 181	C6
-1272	-2^3 * 3 * 53	C2 x C6
-1315	-5 * 263	C6
-1347	-3 * 449	C6
-1363	-29 * 47	C6
-1419	-3 * 11 * 43	C2 x C6
-1432	-2^3 * 179	C6
-1464	-2^3 * 3 * 61	C2 x C6
-1480	-2^3 * 5 * 37	C2 x C6
-1491	-3 * 7 * 71	C2 x C6
-1515	-3 * 5 * 101	C2 x C6
-1547	-7 * 13 * 17	C2 x C6
-1563	-3 * 521	C6
-1572	-2^2 * 3 * 131	C2 x C6
-1588	-2^2 * 397	C6
-1603	-7 * 229	C6
-1668	-2^2 * 3 * 139	C2 x C6
-1720	-2^3 * 5 * 43	C2 x C6
-1812	-2^2 * 3 * 151	C2 x C6
-1843	-19 * 97	C6
-1892	-2^2 * 11 * 43	C2 x C6
-1915	-5 * 383	C6
-1955	-5 * 17 * 23	C2 x C6
-1963	-13 * 151	C6
-1972	-2^2 * 17 * 29	C2 x C6
-2068	-2^2 * 11 * 47	C2 x C6
-2091	-3 * 17 * 41	C2 x C6
-2132	-2^2 * 13 * 41	C2 x C6
-2148	-2^2 * 3 * 179	C2 x C6
-2184	-2^3 * 3 * 7 * 13	C2 x C2 x C6
-2227	-17 * 131	C6
-2235	-3 * 5 * 149	C2 x C6
-2260	-2^2 * 5 * 113	C2 x C6
-2283	-3 * 761	C6
-2355	-3 * 5 * 157	C2 x C6
-2387	-7 * 11 * 31	C2 x C6
-2388	-2^2 * 3 * 199	C2 x C6
-2424	-2^3 * 3 * 101	C2 x C6
-2440	-2^3 * 5 * 61	C2 x C6
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-2472	-2^3 * 3 * 103	C2 x C6
-2515	-5 * 503	C6
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-2920	-2^3 * 5 * 73	C2 x C6
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-3723	-3 * 17 * 73	C2 x C6
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-1172395	-5 * 7 * 19 * 41 * 43	C2 x C2 x C6 x C6
-1185240	-2^3 * 3 * 5 * 7 * 17 * 83	C2 x C2 x C2 x C6 x C6
-1196052	-2^2 * 3 * 11 * 13 * 17 * 41	C2 x C2 x C2 x C6 x C6
-1199220	-2^2 * 3 * 5 * 11 * 23 * 79	C2 x C2 x C2 x C6 x C6
-1282260	-2^2 * 3 * 5 * 7 * 43 * 71	C2 x C2 x C2 x C6 x C6
-1702155	-3 * 5 * 7 * 13 * 29 * 43	C2 x C2 x C2 x C6 x C6
-3892980	-2^2 * 3 * 5 * 7 * 13 * 23 * 31	C2 x C2 x C2 x C2 x C6 x C6
-4696692	-2^2 * 3 * 7 * 11 * 13 * 17 * 23	C2 x C2 x C2 x C2 x C6 x C6
-5761140	-2^2 * 3 * 5 * 7 * 11 * 29 * 43	C2 x C2 x C2 x C2 x C6 x C6

Liste von 33 Körpern mit Exponent 7

Die folgende Tabelle ist nur bis zur Diskriminante 3.1 * 10 ^ 20 vollständig.

Diskriminante	Faktorisierung	Klassengruppe
-71	-71	C7
-151	-151	C7
-223	-223	C7
-251	-251	C7
-463	-463	C7
-467	-467	C7
-487	-487	C7
-587	-587	C7
-811	-811	C7
-827	-827	C7
-859	-859	C7
-1163	-1163	C7
-1171	-1171	C7
-1483	-1483	C7
-1523	-1523	C7
-1627	-1627	C7
-1787	-1787	C7
-1987	-1987	C7
-2011	-2011	C7
-2083	-2083	C7
-2179	-2179	C7
-2251	-2251	C7
-2467	-2467	C7
-2707	-2707	C7
-3019	-3019	C7
-3067	-3067	C7
-3187	-3187	C7
-3907	-3907	C7
-4603	-4603	C7
-5107	-5107	C7
-5923	-5923	C7
-63499	-63499	C7 x C7
-118843	-118843	C7 x C7

Liste von 778 Körpern mit Exponent 8

Die folgende Tabelle ist vollständig, sofern es keine Siegel-Nullstellen gibt. Ohne Annahme einer Vermutung könnte ein Körper fehlen.

Diskriminante	Faktorisierung	Klassengruppe
-95	-5 * 19	C8
-111	-3 * 37	C8
-164	-2^2 * 41	C8
-183	-3 * 61	C8
-248	-2^3 * 31	C8
-295	-5 * 59	C8
-299	-13 * 23	C8
-371	-7 * 53	C8
-376	-2^3 * 47	C8
-395	-5 * 79	C8
-399	-3 * 7 * 19	C2 x C8
-452	-2^2 * 113	C8
-548	-2^2 * 137	C8
-579	-3 * 193	C8
-583	-11 * 53	C8
-632	-2^3 * 79	C8
-644	-2^2 * 7 * 23	C2 x C8
-663	-3 * 13 * 17	C2 x C8
-712	-2^3 * 89	C8
-740	-2^2 * 5 * 37	C2 x C8
-884	-2^2 * 13 * 17	C2 x C8
-903	-3 * 7 * 43	C2 x C8
-904	-2^3 * 113	C8
-939	-3 * 313	C8
-979	-11 * 89	C8
-995	-5 * 199	C8
-1015	-5 * 7 * 29	C2 x C8
-1023	-3 * 11 * 31	C2 x C8
-1043	-7 * 149	C8
-1195	-5 * 239	C8
-1220	-2^2 * 5 * 61	C2 x C8
-1252	-2^2 * 313	C8
-1299	-3 * 433	C8
-1339	-13 * 103	C8
-1348	-2^2 * 337	C8
-1416	-2^3 * 3 * 59	C2 x C8
-1508	-2^2 * 13 * 29	C2 x C8
-1528	-2^3 * 191	C8
-1595	-5 * 11 * 29	C2 x C8
-1608	-2^3 * 3 * 67	C2 x C8
-1624	-2^3 * 7 * 29	C2 x C8
-1640	-2^3 * 5 * 41	C2 x C8
-1651	-13 * 127	C8
-1731	-3 * 577	C8
-1795	-5 * 359	C8
-1803	-3 * 601	C8
-1828	-2^2 * 457	C8
-1864	-2^3 * 233	C8
-1876	-2^2 * 7 * 67	C2 x C8
-1912	-2^3 * 239	C8
-1924	-2^2 * 13 * 37	C2 x C8
-1939	-7 * 277	C8
-2004	-2^2 * 3 * 167	C2 x C8
-2059	-29 * 71	C8
-2072	-2^3 * 7 * 37	C2 x C8
-2211	-3 * 11 * 67	C2 x C8
-2248	-2^3 * 281	C8
-2292	-2^2 * 3 * 191	C2 x C8
-2296	-2^3 * 7 * 41	C2 x C8
-2307	-3 * 769	C8
-2308	-2^2 * 577	C8
-2323	-23 * 101	C8
-2328	-2^3 * 3 * 97	C2 x C8
-2356	-2^2 * 19 * 31	C2 x C8
-2395	-5 * 479	C8
-2419	-41 * 59	C8
-2568	-2^3 * 3 * 107	C2 x C8
-2584	-2^3 * 17 * 19	C2 x C8
-2587	-13 * 199	C8
-2611	-7 * 373	C8
-2739	-3 * 11 * 83	C2 x C8
-2827	-11 * 257	C8
-2868	-2^2 * 3 * 239	C2 x C8
-2884	-2^2 * 7 * 103	C2 x C8
-2947	-7 * 421	C8
-2980	-2^2 * 5 * 149	C2 x C8
-2995	-5 * 599	C8
-3080	-2^3 * 5 * 7 * 11	C2 x C2 x C8
-3140	-2^2 * 5 * 157	C2 x C8
-3144	-2^3 * 3 * 131	C2 x C8
-3160	-2^3 * 5 * 79	C2 x C8
-3171	-3 * 7 * 151	C2 x C8
-3336	-2^3 * 3 * 139	C2 x C8
-3363	-3 * 19 * 59	C2 x C8
-3403	-41 * 83	C8
-3435	-3 * 5 * 229	C2 x C8
-3448	-2^3 * 431	C8
-3460	-2^2 * 5 * 173	C2 x C8
-3531	-3 * 11 * 107	C2 x C8
-3556	-2^2 * 7 * 127	C2 x C8
-3595	-5 * 719	C8
-3732	-2^2 * 3 * 311	C2 x C8
-3752	-2^3 * 7 * 67	C2 x C8
-3784	-2^3 * 11 * 43	C2 x C8
-3787	-7 * 541	C8
-3819	-3 * 19 * 67	C2 x C8
-3883	-11 * 353	C8
-3939	-3 * 13 * 101	C2 x C8
-3963	-3 * 1321	C8
-3976	-2^3 * 7 * 71	C2 x C8
-4008	-2^3 * 3 * 167	C2 x C8
-4179	-3 * 7 * 199	C2 x C8
-4195	-5 * 839	C8
-4216	-2^3 * 17 * 31	C2 x C8
-4228	-2^2 * 7 * 151	C2 x C8
-4251	-3 * 13 * 109	C2 x C8
-4267	-17 * 251	C8
-4324	-2^2 * 23 * 47	C2 x C8
-4340	-2^2 * 5 * 7 * 31	C2 x C2 x C8
-4387	-41 * 107	C8
-4596	-2^2 * 3 * 383	C2 x C8
-4683	-3 * 7 * 223	C2 x C8
-4712	-2^3 * 19 * 31	C2 x C8
-4747	-47 * 101	C8
-4843	-29 * 167	C8
-4867	-31 * 157	C8
-4884	-2^2 * 3 * 11 * 37	C2 x C2 x C8
-4899	-3 * 23 * 71	C2 x C8
-4980	-2^2 * 3 * 5 * 83	C2 x C2 x C8
-4984	-2^3 * 7 * 89	C2 x C8
-5380	-2^2 * 5 * 269	C2 x C8
-5428	-2^2 * 23 * 59	C2 x C8
-5572	-2^2 * 7 * 199	C2 x C8
-5587	-37 * 151	C8
-5640	-2^3 * 3 * 5 * 47	C2 x C2 x C8
-5668	-2^2 * 13 * 109	C2 x C8
-5707	-13 * 439	C8
-5720	-2^3 * 5 * 11 * 13	C2 x C2 x C8
-5795	-5 * 19 * 61	C4 x C8
-5848	-2^3 * 17 * 43	C2 x C8
-5860	-2^2 * 5 * 293	C2 x C8
-5883	-3 * 37 * 53	C2 x C8
-5896	-2^3 * 11 * 67	C2 x C8
-5907	-3 * 11 * 179	C2 x C8
-5908	-2^2 * 7 * 211	C2 x C8
-5947	-19 * 313	C8
-5992	-2^3 * 7 * 107	C2 x C8
-5995	-5 * 11 * 109	C2 x C8
-6040	-2^3 * 5 * 151	C2 x C8
-6099	-3 * 19 * 107	C2 x C8
-6148	-2^2 * 29 * 53	C2 x C8
-6312	-2^3 * 3 * 263	C2 x C8
-6315	-3 * 5 * 421	C2 x C8
-6392	-2^3 * 17 * 47	C4 x C8
-6440	-2^3 * 5 * 7 * 23	C2 x C2 x C8
-6532	-2^2 * 23 * 71	C2 x C8
-6747	-3 * 13 * 173	C2 x C8
-6771	-3 * 37 * 61	C2 x C8
-6792	-2^3 * 3 * 283	C2 x C8
-6868	-2^2 * 17 * 101	C2 x C8
-6923	-7 * 23 * 43	C2 x C8
-6952	-2^3 * 11 * 79	C2 x C8
-7059	-3 * 13 * 181	C4 x C8
-7176	-2^3 * 3 * 13 * 23	C2 x C2 x C8
-7347	-3 * 31 * 79	C2 x C8
-7368	-2^3 * 3 * 307	C2 x C8
-7491	-3 * 11 * 227	C2 x C8
-7579	-11 * 13 * 53	C2 x C8
-7588	-2^2 * 7 * 271	C2 x C8
-7707	-3 * 7 * 367	C2 x C8
-7752	-2^3 * 3 * 17 * 19	C2 x C2 x C8
-7780	-2^2 * 5 * 389	C2 x C8
-7828	-2^2 * 19 * 103	C2 x C8
-7843	-11 * 23 * 31	C2 x C8
-7896	-2^3 * 3 * 7 * 47	C2 x C2 x C8
-7923	-3 * 19 * 139	C2 x C8
-8040	-2^3 * 3 * 5 * 67	C2 x C2 x C8
-8043	-3 * 7 * 383	C2 x C8
-8184	-2^3 * 3 * 11 * 31	C2 x C2 x C8
-8283	-3 * 11 * 251	C2 x C8
-8308	-2^2 * 31 * 67	C2 x C8
-8340	-2^2 * 3 * 5 * 139	C2 x C2 x C8
-8515	-5 * 13 * 131	C2 x C8
-8520	-2^3 * 3 * 5 * 71	C2 x C2 x C8
-8555	-5 * 29 * 59	C4 x C8
-8635	-5 * 11 * 157	C2 x C8
-8643	-3 * 43 * 67	C2 x C8
-8968	-2^3 * 19 * 59	C2 x C8
-9060	-2^2 * 3 * 5 * 151	C2 x C2 x C8
-9156	-2^2 * 3 * 7 * 109	C2 x C2 x C8
-9219	-3 * 7 * 439	C2 x C8
-9316	-2^2 * 17 * 137	C4 x C8
-9348	-2^2 * 3 * 19 * 41	C2 x C2 x C8
-9412	-2^2 * 13 * 181	C2 x C8
-9435	-3 * 5 * 17 * 37	C2 x C2 x C8
-9460	-2^2 * 5 * 11 * 43	C2 x C2 x C8
-9483	-3 * 29 * 109	C2 x C8
-9588	-2^2 * 3 * 17 * 47	C2 x C2 x C8
-9640	-2^3 * 5 * 241	C2 x C8
-9768	-2^3 * 3 * 11 * 37	C2 x C2 x C8
-9780	-2^2 * 3 * 5 * 163	C2 x C2 x C8
-9835	-5 * 7 * 281	C2 x C8
-9860	-2^2 * 5 * 17 * 29	C2 x C2 x C8
-9880	-2^3 * 5 * 13 * 19	C2 x C2 x C8
-9912	-2^3 * 3 * 7 * 59	C2 x C2 x C8
-9960	-2^3 * 3 * 5 * 83	C2 x C2 x C8
-10132	-2^2 * 17 * 149	C2 x C8
-10203	-3 * 19 * 179	C2 x C8
-10227	-3 * 7 * 487	C2 x C8
-10387	-13 * 17 * 47	C2 x C8
-10420	-2^2 * 5 * 521	C2 x C8
-10563	-3 * 7 * 503	C2 x C8
-10635	-3 * 5 * 709	C2 x C8
-10660	-2^2 * 5 * 13 * 41	C2 x C2 x C8
-10824	-2^3 * 3 * 11 * 41	C2 x C2 x C8
-10868	-2^2 * 11 * 13 * 19	C2 x C2 x C8
-11092	-2^2 * 47 * 59	C2 x C8
-11284	-2^2 * 7 * 13 * 31	C2 x C2 x C8
-11316	-2^2 * 3 * 23 * 41	C2 x C2 x C8
-11460	-2^2 * 3 * 5 * 191	C2 x C2 x C8
-11523	-3 * 23 * 167	C2 x C8
-11571	-3 * 7 * 19 * 29	C2 x C2 x C8
-11572	-2^2 * 11 * 263	C2 x C8
-11635	-5 * 13 * 179	C2 x C8
-11739	-3 * 7 * 13 * 43	C2 x C2 x C8
-11832	-2^3 * 3 * 17 * 29	C2 x C2 x C8
-11940	-2^2 * 3 * 5 * 199	C2 x C2 x C8
-12027	-3 * 19 * 211	C2 x C8
-12040	-2^3 * 5 * 7 * 43	C2 x C2 x C8
-12084	-2^2 * 3 * 19 * 53	C2 x C2 x C8
-12259	-13 * 23 * 41	C2 x C8
-12580	-2^2 * 5 * 17 * 37	C2 x C2 x C8
-12660	-2^2 * 3 * 5 * 211	C2 x C2 x C8
-12747	-3 * 7 * 607	C2 x C8
-12772	-2^2 * 31 * 103	C2 x C8
-12792	-2^3 * 3 * 13 * 41	C2 x C2 x C8
-12804	-2^2 * 3 * 11 * 97	C2 x C2 x C8
-12835	-5 * 17 * 151	C2 x C8
-12840	-2^3 * 3 * 5 * 107	C2 x C2 x C8
-12859	-7 * 11 * 167	C2 x C8
-12948	-2^2 * 3 * 13 * 83	C2 x C2 x C8
-13048	-2^3 * 7 * 233	C4 x C8
-13192	-2^3 * 17 * 97	C2 x C8
-13272	-2^3 * 3 * 7 * 79	C2 x C2 x C8
-13288	-2^3 * 11 * 151	C2 x C8
-13332	-2^2 * 3 * 11 * 101	C2 x C2 x C8
-13363	-7 * 23 * 83	C2 x C8
-13432	-2^3 * 23 * 73	C4 x C8
-13515	-3 * 5 * 17 * 53	C2 x C2 x C8
-13560	-2^3 * 3 * 5 * 113	C2 x C2 x C8
-13755	-3 * 5 * 7 * 131	C2 x C2 x C8
-13795	-5 * 31 * 89	C2 x C8
-13827	-3 * 11 * 419	C2 x C8
-13908	-2^2 * 3 * 19 * 61	C2 x C2 x C8
-14388	-2^2 * 3 * 11 * 109	C2 x C2 x C8
-14707	-7 * 11 * 191	C2 x C8
-14795	-5 * 11 * 269	C4 x C8
-15067	-13 * 19 * 61	C2 x C8
-15387	-3 * 23 * 223	C2 x C8
-15715	-5 * 7 * 449	C2 x C8
-15736	-2^3 * 7 * 281	C4 x C8
-16008	-2^3 * 3 * 23 * 29	C2 x C2 x C8
-16027	-11 * 31 * 47	C2 x C8
-16195	-5 * 41 * 79	C2 x C8
-16212	-2^2 * 3 * 7 * 193	C2 x C2 x C8
-16440	-2^3 * 3 * 5 * 137	C2 x C2 x C8
-16548	-2^2 * 3 * 7 * 197	C2 x C2 x C8
-16692	-2^2 * 3 * 13 * 107	C2 x C2 x C8
-16779	-3 * 7 * 17 * 47	C2 x C2 x C8
-16835	-5 * 7 * 13 * 37	C2 x C2 x C8
-16995	-3 * 5 * 11 * 103	C2 x C2 x C8
-17080	-2^3 * 5 * 7 * 61	C2 x C2 x C8
-17112	-2^3 * 3 * 23 * 31	C2 x C2 x C8
-17115	-3 * 5 * 7 * 163	C2 x C2 x C8
-17227	-7 * 23 * 107	C2 x C8
-17272	-2^3 * 17 * 127	C4 x C8
-17347	-11 * 19 * 83	C2 x C8
-17355	-3 * 5 * 13 * 89	C2 x C2 x C8
-17515	-5 * 31 * 113	C2 x C8
-17688	-2^3 * 3 * 11 * 67	C2 x C2 x C8
-17880	-2^3 * 3 * 5 * 149	C2 x C2 x C8
-18291	-3 * 7 * 13 * 67	C2 x C2 x C8
-18403	-7 * 11 * 239	C2 x C8
-18408	-2^3 * 3 * 13 * 59	C2 x C2 x C8
-18532	-2^2 * 41 * 113	C4 x C8
-18564	-2^2 * 3 * 7 * 13 * 17	C2 x C2 x C2 x C8
-18676	-2^2 * 7 * 23 * 29	C2 x C2 x C8
-18715	-5 * 19 * 197	C2 x C8
-18760	-2^3 * 5 * 7 * 67	C2 x C2 x C8
-18907	-7 * 37 * 73	C2 x C8
-19108	-2^2 * 17 * 281	C4 x C8
-19195	-5 * 11 * 349	C2 x C8
-19227	-3 * 13 * 17 * 29	C2 x C2 x C8
-19272	-2^3 * 3 * 11 * 73	C2 x C2 x C8
-19560	-2^3 * 3 * 5 * 163	C2 x C2 x C8
-19608	-2^3 * 3 * 19 * 43	C2 x C2 x C8
-19720	-2^3 * 5 * 17 * 29	C2 x C2 x C8
-19812	-2^2 * 3 * 13 * 127	C2 x C2 x C8
-19987	-11 * 23 * 79	C2 x C8
-19995	-3 * 5 * 31 * 43	C2 x C2 x C8
-20091	-3 * 37 * 181	C4 x C8
-20163	-3 * 11 * 13 * 47	C2 x C2 x C8
-20235	-3 * 5 * 19 * 71	C2 x C2 x C8
-20740	-2^2 * 5 * 17 * 61	C2 x C2 x C8
-20760	-2^3 * 3 * 5 * 173	C2 x C4 x C8
-20868	-2^2 * 3 * 37 * 47	C2 x C2 x C8
-21147	-3 * 7 * 19 * 53	C2 x C2 x C8
-21243	-3 * 73 * 97	C4 x C8
-21571	-11 * 37 * 53	C4 x C8
-21715	-5 * 43 * 101	C2 x C8
-21736	-2^3 * 11 * 13 * 19	C2 x C2 x C8
-21828	-2^2 * 3 * 17 * 107	C2 x C2 x C8
-21835	-5 * 11 * 397	C2 x C8
-21912	-2^3 * 3 * 11 * 83	C2 x C2 x C8
-22152	-2^3 * 3 * 13 * 71	C2 x C2 x C8
-22155	-3 * 5 * 7 * 211	C2 x C2 x C8
-22243	-13 * 29 * 59	C2 x C8
-22360	-2^3 * 5 * 13 * 43	C2 x C2 x C8
-22372	-2^2 * 7 * 17 * 47	C2 x C2 x C8
-22420	-2^2 * 5 * 19 * 59	C2 x C2 x C8
-22456	-2^3 * 7 * 401	C4 x C8
-22515	-3 * 5 * 19 * 79	C2 x C2 x C8
-22632	-2^3 * 3 * 23 * 41	C2 x C2 x C8
-22740	-2^2 * 3 * 5 * 379	C2 x C2 x C8
-22763	-13 * 17 * 103	C4 x C8
-22792	-2^3 * 7 * 11 * 37	C2 x C2 x C8
-22971	-3 * 13 * 19 * 31	C2 x C2 x C8
-23028	-2^2 * 3 * 19 * 101	C2 x C2 x C8
-23140	-2^2 * 5 * 13 * 89	C2 x C2 x C8
-23155	-5 * 11 * 421	C4 x C8
-23268	-2^2 * 3 * 7 * 277	C2 x C2 x C8
-23380	-2^2 * 5 * 7 * 167	C2 x C2 x C8
-23460	-2^2 * 3 * 5 * 17 * 23	C2 x C2 x C2 x C8
-23835	-3 * 5 * 7 * 227	C2 x C2 x C8
-23892	-2^2 * 3 * 11 * 181	C2 x C2 x C8
-23944	-2^3 * 41 * 73	C4 x C8
-24004	-2^2 * 17 * 353	C4 x C8
-24024	-2^3 * 3 * 7 * 11 * 13	C2 x C2 x C2 x C8
-24035	-5 * 11 * 19 * 23	C2 x C2 x C8
-24168	-2^3 * 3 * 19 * 53	C2 x C2 x C8
-24472	-2^3 * 7 * 19 * 23	C2 x C2 x C8
-25080	-2^3 * 3 * 5 * 11 * 19	C2 x C2 x C2 x C8
-25419	-3 * 37 * 229	C4 x C8
-25620	-2^2 * 3 * 5 * 7 * 61	C2 x C2 x C2 x C8
-25960	-2^3 * 5 * 11 * 59	C2 x C2 x C8
-25988	-2^2 * 73 * 89	C8 x C8
-26180	-2^2 * 5 * 7 * 11 * 17	C2 x C2 x C2 x C8
-26488	-2^3 * 7 * 11 * 43	C2 x C2 x C8
-26772	-2^2 * 3 * 23 * 97	C2 x C2 x C8
-26980	-2^2 * 5 * 19 * 71	C2 x C2 x C8
-27307	-7 * 47 * 83	C2 x C8
-27412	-2^2 * 7 * 11 * 89	C2 x C2 x C8
-28083	-3 * 11 * 23 * 37	C2 x C2 x C8
-28120	-2^3 * 5 * 19 * 37	C2 x C2 x C8
-28203	-3 * 7 * 17 * 79	C2 x C2 x C8
-28308	-2^2 * 3 * 7 * 337	C2 x C2 x C8
-28840	-2^3 * 5 * 7 * 103	C2 x C2 x C8
-29380	-2^2 * 5 * 13 * 113	C2 x C2 x C8
-29512	-2^3 * 7 * 17 * 31	C2 x C2 x C8
-29523	-3 * 13 * 757	C4 x C8
-29667	-3 * 11 * 29 * 31	C2 x C2 x C8
-29892	-2^2 * 3 * 47 * 53	C2 x C2 x C8
-30328	-2^3 * 17 * 223	C4 x C8
-30552	-2^3 * 3 * 19 * 67	C2 x C2 x C8
-30580	-2^2 * 5 * 11 * 139	C2 x C2 x C8
-31080	-2^3 * 3 * 5 * 7 * 37	C2 x C2 x C2 x C8
-31515	-3 * 5 * 11 * 191	C2 x C2 x C8
-31668	-2^2 * 3 * 7 * 13 * 29	C2 x C2 x C2 x C8
-31864	-2^3 * 7 * 569	C8 x C8
-32235	-3 * 5 * 7 * 307	C2 x C2 x C8
-32331	-3 * 13 * 829	C8 x C8
-32395	-5 * 11 * 19 * 31	C2 x C2 x C8
-33288	-2^3 * 3 * 19 * 73	C2 x C4 x C8
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-566040	-2^3 * 3 * 5 * 53 * 89	C2 x C2 x C8 x C8
-568888	-2^3 * 17 * 47 * 89	C4 x C4 x C8
-585915	-3 * 5 * 11 * 53 * 67	C2 x C2 x C4 x C8
-590835	-3 * 5 * 7 * 17 * 331	C2 x C2 x C4 x C8
-603988	-2^2 * 7 * 11 * 37 * 53	C2 x C2 x C4 x C8
-611403	-3 * 13 * 61 * 257	C2 x C8 x C8
-630147	-3 * 7 * 37 * 811	C2 x C8 x C8
-644280	-2^3 * 3 * 5 * 7 * 13 * 59	C2 x C2 x C2 x C4 x C8
-646195	-5 * 11 * 31 * 379	C2 x C8 x C8
-674520	-2^3 * 3 * 5 * 7 * 11 * 73	C2 x C2 x C2 x C4 x C8
-688755	-3 * 5 * 17 * 37 * 73	C2 x C2 x C4 x C8
-692692	-2^2 * 7 * 11 * 13 * 173	C2 x C2 x C4 x C8
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-705432	-2^3 * 3 * 7 * 13 * 17 * 19	C2 x C2 x C2 x C4 x C8
-713883	-3 * 47 * 61 * 83	C2 x C8 x C8
-743028	-2^2 * 3 * 11 * 13 * 433	C2 x C2 x C8 x C8
-788307	-3 * 13 * 17 * 29 * 41	C2 x C2 x C4 x C8
-806520	-2^3 * 3 * 5 * 11 * 13 * 47	C2 x C2 x C2 x C4 x C8
-809115	-3 * 5 * 17 * 19 * 167	C2 x C2 x C8 x C8
-834360	-2^3 * 3 * 5 * 17 * 409	C2 x C2 x C8 x C8
-844440	-2^3 * 3 * 5 * 31 * 227	C2 x C2 x C8 x C8
-850795	-5 * 11 * 31 * 499	C2 x C8 x C8
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-1115268	-2^2 * 3 * 7 * 11 * 17 * 71	C2 x C2 x C2 x C4 x C8
-1232340	-2^2 * 3 * 5 * 19 * 23 * 47	C2 x C2 x C2 x C4 x C8
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-1408740	-2^2 * 3 * 5 * 53 * 443	C2 x C2 x C8 x C8
-1446907	-7 * 11 * 19 * 23 * 43	C2 x C2 x C4 x C8
-1472115	-3 * 5 * 17 * 23 * 251	C2 x C2 x C8 x C8
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-1519960	-2^3 * 5 * 13 * 37 * 79	C2 x C2 x C8 x C8
-1562484	-2^2 * 3 * 7 * 11 * 19 * 89	C2 x C2 x C2 x C8 x C8
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-1592115	-3 * 5 * 7 * 59 * 257	C2 x C2 x C8 x C8
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-1842715	-5 * 7 * 17 * 19 * 163	C2 x C2 x C8 x C8
-1928595	-3 * 5 * 19 * 67 * 101	C2 x C2 x C8 x C8
-1935507	-3 * 7 * 37 * 47 * 53	C2 x C2 x C8 x C8
-1937635	-5 * 7 * 23 * 29 * 83	C2 x C2 x C8 x C8
-2043195	-3 * 5 * 7 * 11 * 29 * 61	C2 x C2 x C2 x C4 x C8
-2045323	-7 * 37 * 53 * 149	C4 x C4 x C8
-2078440	-2^3 * 5 * 7 * 13 * 571	C2 x C2 x C8 x C8
-2095060	-2^2 * 5 * 11 * 89 * 107	C2 x C2 x C8 x C8
-2103220	-2^2 * 5 * 7 * 83 * 181	C2 x C2 x C8 x C8
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-2188920	-2^3 * 3 * 5 * 17 * 29 * 37	C2 x C2 x C4 x C4 x C8
-2209467	-3 * 13 * 181 * 313	C4 x C8 x C8
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-2401867	-13 * 23 * 29 * 277	C4 x C8 x C8
-2420635	-5 * 7 * 23 * 31 * 97	C2 x C2 x C8 x C8
-2443155	-3 * 5 * 11 * 13 * 17 * 67	C2 x C2 x C2 x C4 x C8
-2523928	-2^3 * 11 * 23 * 29 * 43	C2 x C2 x C8 x C8
-2999560	-2^3 * 5 * 31 * 41 * 59	C2 x C2 x C8 x C8
-3040888	-2^3 * 41 * 73 * 127	C4 x C8 x C8
-3081540	-2^2 * 3 * 5 * 7 * 11 * 23 * 29	C2 x C2 x C2 x C2 x C4 x C8
-3121035	-3 * 5 * 19 * 47 * 233	C2 x C2 x C8 x C8
-3352020	-2^2 * 3 * 5 * 7 * 23 * 347	C2 x C2 x C2 x C8 x C8
-3452020	-2^2 * 5 * 11 * 13 * 17 * 71	C2 x C2 x C2 x C8 x C8
-3468595	-5 * 13 * 17 * 43 * 73	C2 x C2 x C8 x C8
-3536260	-2^2 * 5 * 7 * 13 * 29 * 67	C2 x C2 x C2 x C8 x C8
-3598980	-2^2 * 3 * 5 * 7 * 11 * 19 * 41	C2 x C2 x C2 x C2 x C4 x C8
-3608760	-2^3 * 3 * 5 * 17 * 29 * 61	C2 x C2 x C2 x C8 x C8
-4800772	-2^2 * 41 * 73 * 401	C4 x C8 x C8
-4886995	-5 * 31 * 41 * 769	C4 x C8 x C8
-4903395	-3 * 5 * 7 * 17 * 41 * 67	C2 x C2 x C2 x C8 x C8
-5358340	-2^2 * 5 * 13 * 37 * 557	C2 x C4 x C8 x C8
-5692440	-2^3 * 3 * 5 * 13 * 41 * 89	C2 x C2 x C4 x C8 x C8
-6005748	-2^2 * 3 * 7 * 19 * 53 * 71	C2 x C2 x C2 x C8 x C8
-6174168	-2^3 * 3 * 7 * 11 * 13 * 257	C2 x C2 x C2 x C8 x C8
-6585987	-3 * 17 * 29 * 61 * 73	C2 x C2 x C8 x C8
-7538388	-2^2 * 3 * 11 * 13 * 23 * 191	C2 x C2 x C2 x C8 x C8
-11148180	-2^2 * 3 * 5 * 29 * 43 * 149	C2 x C2 x C4 x C8 x C8
-12517428	-2^2 * 3 * 7 * 11 * 19 * 23 * 31	C2 x C2 x C2 x C4 x C4 x C8
-15337315	-5 * 7 * 17 * 149 * 173	C2 x C4 x C8 x C8
-15898740	-2^2 * 3 * 5 * 11 * 13 * 17 * 109	C2 x C2 x C2 x C2 x C8 x C8
-17168515	-5 * 7 * 13 * 97 * 389	C2 x C4 x C8 x C8
-28663635	-3 * 5 * 7 * 11 * 13 * 23 * 83	C2 x C2 x C2 x C2 x C8 x C8
-29493555	-3 * 5 * 7 * 13 * 17 * 31 * 41	C2 x C2 x C2 x C2 x C8 x C8
-31078723	-13 * 43 * 53 * 1049	C8 x C8 x C8
-430950520	-2^3 * 5 * 7 * 11 * 13 * 47 * 229	C2 x C2 x C2 x C8 x C8 x C8

Sie interessieren sich für:

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.

Smallest Split fixed.c

No small split.c

List of fields

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.

Download Datei

Ima­gi­nä­r­qua­dra­ti­sche Zahl­kör­per mit klei­nem Ex­po­nen­ten

Sie interessieren sich für:

C-Programme

Julia Programme

Imaginärquadratische Zahlkörper mit kleinem Exponenten