Ima­gin­ary quad­rat­ic num­ber fields with small ex­po­nent.

Here are lists with imaginary quadratic fields with exponent of the ideal class group up to 8. For exponent 1 the list is complete. For exponents 2,4,8 the lists are complete assuming that there are no Siegel zeros. Without this assumption there might be one missing field. For exponents 3 and 5 the lists are complete assuming the generalized Riemann hypothesis. Without this assumption it is known that there are finitely many fields with exponent 3 or 5. For exponent 6 the list is complete up to discriminant 3.1·1020. It is known that there are finitely many fields with exponent 6. For exponent 7 the list is complete up to discriminant 3.1·1020. It is not known whether there are only finitely many fields with exponent 7. Assuming the generalized Riemann hypothesis the exponent tends to infinity, hence there should be only finitely many fields with given exponent.

The scientific content is given in the paper:

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

The following table contains all fields with exponent 1.

Discriminant Factorization Class group
-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

The following table is complete assuming that there are no Siegel zeros. Without any assumption there might be one missing field.

Discriminant Factorization Class group
-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

The following table is complete assuming that the generalized Riemann hypothesis is true. Without any assumption it is known that the list should be finite.

Discriminant Factorization Class group
-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

The following table is complete assuming that there are no Siegel zeros. Without any assumption there might be one missing field.

Discriminant Factorization Class group
-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

The following table is complete assuming that the generalized Riemann hypothesis is true. Without any assumption it is known that the list should be finite.

Discriminant Factorization Class group
-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

The following table is only complete up to discriminant 3.1*10^20. It is unconditionally known that there is only a finite number of fields with exponent 6.

Discriminant Factorization Class group
-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
-2443 -7 * 349 C6
-2472 -2^3 * 3 * 103 C2 x C6
-2515 -5 * 503 C6
-2555 -5 * 7 * 73 C2 x C6
-2563 -11 * 233 C6
-2595 -3 * 5 * 173 C2 x C6
-2635 -5 * 17 * 31 C2 x C6
-2660 -2^2 * 5 * 7 * 19 C2 x C2 x C6
-2676 -2^2 * 3 * 223 C2 x C6
-2680 -2^3 * 5 * 67 C2 x C6
-2728 -2^3 * 11 * 31 C2 x C6
-2740 -2^2 * 5 * 137 C2 x C6
-2787 -3 * 929 C6
-2795 -5 * 13 * 43 C2 x C6
-2820 -2^2 * 3 * 5 * 47 C2 x C2 x C6
-2856 -2^3 * 3 * 7 * 17 C2 x C2 x C6
-2920 -2^3 * 5 * 73 C2 x C6
-2923 -37 * 79 C6
-2955 -3 * 5 * 197 C2 x C6
-2964 -2^2 * 3 * 13 * 19 C2 x C2 x C6
-3012 -2^2 * 3 * 251 C2 x C6
-3048 -2^3 * 3 * 127 C2 x C6
-3115 -5 * 7 * 89 C2 x C6
-3235 -5 * 647 C6
-3252 -2^2 * 3 * 271 C2 x C6
-3256 -2^3 * 11 * 37 C2 x C6
-3268 -2^2 * 19 * 43 C2 x C6
-3304 -2^3 * 7 * 59 C2 x C6
-3427 -23 * 149 C6
-3444 -2^2 * 3 * 7 * 41 C2 x C2 x C6
-3451 -7 * 17 * 29 C2 x C6
-3523 -13 * 271 C6
-3540 -2^2 * 3 * 5 * 59 C2 x C2 x C6
-3619 -7 * 11 * 47 C2 x C6
-3652 -2^2 * 11 * 83 C2 x C6
-3720 -2^3 * 3 * 5 * 31 C2 x C2 x C6
-3723 -3 * 17 * 73 C2 x C6
-3763 -53 * 71 C6
-3768 -2^3 * 3 * 157 C2 x C6
-3796 -2^2 * 13 * 73 C2 x C6
-3835 -5 * 13 * 59 C2 x C6
-3864 -2^3 * 3 * 7 * 23 C2 x C2 x C6
-3876 -2^2 * 3 * 17 * 19 C2 x C2 x C6
-3880 -2^3 * 5 * 97 C2 x C6
-3892 -2^2 * 7 * 139 C2 x C6
-3955 -5 * 7 * 113 C2 x C6
-3972 -2^2 * 3 * 331 C2 x C6
-4035 -3 * 5 * 269 C2 x C6
-4120 -2^3 * 5 * 103 C2 x C6
-4147 -11 * 13 * 29 C2 x C6
-4152 -2^3 * 3 * 173 C2 x C6
-4155 -3 * 5 * 277 C2 x C6
-4360 -2^3 * 5 * 109 C2 x C6
-4587 -3 * 11 * 139 C2 x C6
-4648 -2^3 * 7 * 83 C2 x C6
-4692 -2^2 * 3 * 17 * 23 C2 x C2 x C6
-4708 -2^2 * 11 * 107 C2 x C6
-4755 -3 * 5 * 317 C2 x C6
-4795 -5 * 7 * 137 C2 x C6
-4872 -2^3 * 3 * 7 * 29 C2 x C2 x C6
-4888 -2^3 * 13 * 47 C2 x C6
-4920 -2^3 * 3 * 5 * 41 C2 x C2 x C6
-4947 -3 * 17 * 97 C2 x C6
-5016 -2^3 * 3 * 11 * 19 C2 x C2 x C6
-5032 -2^3 * 17 * 37 C2 x C6
-5035 -5 * 19 * 53 C2 x C6
-5124 -2^2 * 3 * 7 * 61 C2 x C2 x C6
-5140 -2^2 * 5 * 257 C2 x C6
-5236 -2^2 * 7 * 11 * 17 C2 x C2 x C6
-5307 -3 * 29 * 61 C2 x C6
-5320 -2^3 * 5 * 7 * 19 C2 x C2 x C6
-5395 -5 * 13 * 83 C2 x C6
-5523 -3 * 7 * 263 C2 x C6
-5595 -3 * 5 * 373 C2 x C6
-5763 -3 * 17 * 113 C2 x C6
-5811 -3 * 13 * 149 C2 x C6
-5835 -3 * 5 * 389 C2 x C6
-5928 -2^3 * 3 * 13 * 19 C2 x C2 x C6
-6072 -2^3 * 3 * 11 * 23 C2 x C2 x C6
-6132 -2^2 * 3 * 7 * 73 C2 x C2 x C6
-6180 -2^2 * 3 * 5 * 103 C2 x C2 x C6
-6216 -2^3 * 3 * 7 * 37 C2 x C2 x C6
-6232 -2^3 * 19 * 41 C2 x C6
-6235 -5 * 29 * 43 C2 x C6
-6555 -3 * 5 * 19 * 23 C2 x C2 x C6
-6603 -3 * 31 * 71 C2 x C6
-6643 -7 * 13 * 73 C2 x C6
-6699 -3 * 7 * 11 * 29 C2 x C2 x C6
-6715 -5 * 17 * 79 C2 x C6
-6888 -2^3 * 3 * 7 * 41 C2 x C2 x C6
-6916 -2^2 * 7 * 13 * 19 C2 x C2 x C6
-6955 -5 * 13 * 107 C2 x C6
-6963 -3 * 11 * 211 C2 x C6
-6987 -3 * 17 * 137 C2 x C6
-7107 -3 * 23 * 103 C2 x C6
-7320 -2^3 * 3 * 5 * 61 C2 x C2 x C6
-7332 -2^2 * 3 * 13 * 47 C2 x C2 x C6
-7620 -2^2 * 3 * 5 * 127 C2 x C2 x C6
-7683 -3 * 13 * 197 C2 x C6
-7912 -2^3 * 23 * 43 C2 x C6
-8148 -2^2 * 3 * 7 * 97 C2 x C2 x C6
-8155 -5 * 7 * 233 C2 x C6
-8211 -3 * 7 * 17 * 23 C2 x C2 x C6
-8260 -2^2 * 5 * 7 * 59 C2 x C2 x C6
-8323 -7 * 29 * 41 C2 x C6
-8395 -5 * 23 * 73 C2 x C6
-8740 -2^2 * 5 * 19 * 23 C2 x C2 x C6
-8760 -2^3 * 3 * 5 * 73 C2 x C2 x C6
-8772 -2^2 * 3 * 17 * 43 C2 x C2 x C6
-8787 -3 * 29 * 101 C2 x C6
-8827 -7 * 13 * 97 C2 x C6
-9048 -2^3 * 3 * 13 * 29 C2 x C2 x C6
-9139 -13 * 19 * 37 C2 x C6
-9384 -2^3 * 3 * 17 * 23 C2 x C2 x C6
-9480 -2^3 * 3 * 5 * 79 C2 x C2 x C6
-9492 -2^2 * 3 * 7 * 113 C2 x C2 x C6
-9672 -2^3 * 3 * 13 * 31 C2 x C2 x C6
-9748 -2^2 * 2437 C3 x C6
-9843 -3 * 17 * 193 C2 x C6
-9940 -2^2 * 5 * 7 * 71 C2 x C2 x C6
-10120 -2^3 * 5 * 11 * 23 C2 x C2 x C6
-10212 -2^2 * 3 * 23 * 37 C2 x C2 x C6
-10248 -2^3 * 3 * 7 * 61 C2 x C2 x C6
-10360 -2^3 * 5 * 7 * 37 C2 x C2 x C6
-10452 -2^2 * 3 * 13 * 67 C2 x C2 x C6
-10488 -2^3 * 3 * 19 * 23 C2 x C2 x C6
-10707 -3 * 43 * 83 C2 x C6
-10740 -2^2 * 3 * 5 * 179 C2 x C2 x C6
-10788 -2^2 * 3 * 29 * 31 C2 x C2 x C6
-10795 -5 * 17 * 127 C2 x C6
-10915 -5 * 37 * 59 C2 x C6
-11155 -5 * 23 * 97 C2 x C6
-11220 -2^2 * 3 * 5 * 11 * 17 C2 x C2 x C2 x C6
-11235 -3 * 5 * 7 * 107 C2 x C2 x C6
-11620 -2^2 * 5 * 7 * 83 C2 x C2 x C6
-11748 -2^2 * 3 * 11 * 89 C2 x C2 x C6
-11803 -11 * 29 * 37 C2 x C6
-11928 -2^3 * 3 * 7 * 71 C2 x C2 x C6
-12067 -11 * 1097 C3 x C6
-12243 -3 * 7 * 11 * 53 C2 x C2 x C6
-12376 -2^3 * 7 * 13 * 17 C2 x C2 x C6
-12408 -2^3 * 3 * 11 * 47 C2 x C2 x C6
-12628 -2^2 * 7 * 11 * 41 C2 x C2 x C6
-12760 -2^3 * 5 * 11 * 29 C2 x C2 x C6
-13035 -3 * 5 * 11 * 79 C2 x C2 x C6
-13080 -2^3 * 3 * 5 * 109 C2 x C2 x C6
-13395 -3 * 5 * 19 * 47 C2 x C2 x C6
-13668 -2^2 * 3 * 17 * 67 C2 x C2 x C6
-13780 -2^2 * 5 * 13 * 53 C2 x C2 x C6
-14212 -2^2 * 11 * 17 * 19 C2 x C2 x C6
-14235 -3 * 5 * 13 * 73 C2 x C2 x C6
-14260 -2^2 * 5 * 23 * 31 C2 x C2 x C6
-14443 -11 * 13 * 101 C2 x C6
-14532 -2^2 * 3 * 7 * 173 C2 x C2 x C6
-14595 -3 * 5 * 7 * 139 C2 x C2 x C6
-14835 -3 * 5 * 23 * 43 C2 x C2 x C6
-14952 -2^3 * 3 * 7 * 89 C2 x C2 x C6
-14980 -2^2 * 5 * 7 * 107 C2 x C2 x C6
-15283 -17 * 29 * 31 C2 x C6
-15540 -2^2 * 3 * 5 * 7 * 37 C2 x C2 x C2 x C6
-15544 -2^3 * 29 * 67 C6 x C6
-15555 -3 * 5 * 17 * 61 C2 x C2 x C6
-15640 -2^3 * 5 * 17 * 23 C2 x C2 x C6
-15652 -2^2 * 7 * 13 * 43 C2 x C2 x C6
-15960 -2^3 * 3 * 5 * 7 * 19 C2 x C2 x C2 x C6
-16107 -3 * 7 * 13 * 59 C2 x C2 x C6
-16627 -13 * 1279 C3 x C6
-16872 -2^3 * 3 * 19 * 37 C2 x C2 x C6
-17043 -3 * 13 * 19 * 23 C2 x C2 x C6
-17131 -37 * 463 C3 x C6
-17160 -2^3 * 3 * 5 * 11 * 13 C2 x C2 x C2 x C6
-17556 -2^2 * 3 * 7 * 11 * 19 C2 x C2 x C2 x C6
-17940 -2^2 * 3 * 5 * 13 * 23 C2 x C2 x C2 x C6
-18040 -2^3 * 5 * 11 * 41 C2 x C2 x C6
-18088 -2^3 * 7 * 17 * 19 C2 x C2 x C6
-18340 -2^2 * 5 * 7 * 131 C2 x C2 x C6
-18555 -3 * 5 * 1237 C6 x C6
-18795 -3 * 5 * 7 * 179 C2 x C2 x C6
-18915 -3 * 5 * 13 * 97 C2 x C2 x C6
-19140 -2^2 * 3 * 5 * 11 * 29 C2 x C2 x C2 x C6
-19651 -43 * 457 C3 x C6
-19803 -3 * 7 * 23 * 41 C2 x C2 x C6
-20355 -3 * 5 * 23 * 59 C2 x C2 x C6
-20568 -2^3 * 3 * 857 C6 x C6
-20955 -3 * 5 * 11 * 127 C2 x C2 x C6
-20995 -5 * 13 * 17 * 19 C2 x C2 x C6
-21112 -2^3 * 7 * 13 * 29 C2 x C2 x C6
-21252 -2^2 * 3 * 7 * 11 * 23 C2 x C2 x C2 x C6
-22260 -2^2 * 3 * 5 * 7 * 53 C2 x C2 x C2 x C6
-22395 -3 * 5 * 1493 C6 x C6
-22440 -2^3 * 3 * 5 * 11 * 17 C2 x C2 x C2 x C6
-22443 -3 * 7481 C3 x C6
-23115 -3 * 5 * 23 * 67 C2 x C2 x C6
-23188 -2^2 * 11 * 17 * 31 C2 x C2 x C6
-23683 -11 * 2153 C3 x C6
-24115 -5 * 7 * 13 * 53 C2 x C2 x C6
-24123 -3 * 11 * 17 * 43 C2 x C2 x C6
-24180 -2^2 * 3 * 5 * 13 * 31 C2 x C2 x C2 x C6
-24340 -2^2 * 5 * 1217 C6 x C6
-24360 -2^3 * 3 * 5 * 7 * 29 C2 x C2 x C2 x C6
-24388 -2^2 * 7 * 13 * 67 C2 x C2 x C6
-24420 -2^2 * 3 * 5 * 11 * 37 C2 x C2 x C2 x C6
-24915 -3 * 5 * 11 * 151 C2 x C2 x C6
-24955 -5 * 7 * 23 * 31 C2 x C2 x C6
-25347 -3 * 7 * 17 * 71 C2 x C2 x C6
-25707 -3 * 11 * 19 * 41 C2 x C2 x C6
-25755 -3 * 5 * 17 * 101 C2 x C2 x C6
-25795 -5 * 7 * 11 * 67 C2 x C2 x C6
-26040 -2^3 * 3 * 5 * 7 * 31 C2 x C2 x C2 x C6
-26187 -3 * 7 * 29 * 43 C2 x C2 x C6
-26520 -2^3 * 3 * 5 * 13 * 17 C2 x C2 x C2 x C6
-26760 -2^3 * 3 * 5 * 223 C2 x C6 x C6
-27060 -2^2 * 3 * 5 * 11 * 41 C2 x C2 x C2 x C6
-27115 -5 * 11 * 17 * 29 C2 x C2 x C6
-27156 -2^2 * 3 * 31 * 73 C2 x C6 x C6
-27435 -3 * 5 * 31 * 59 C2 x C2 x C6
-27640 -2^3 * 5 * 691 C6 x C6
-28644 -2^2 * 3 * 7 * 11 * 31 C2 x C2 x C2 x C6
-29172 -2^2 * 3 * 11 * 13 * 17 C2 x C2 x C2 x C6
-29640 -2^3 * 3 * 5 * 13 * 19 C2 x C2 x C2 x C6
-30360 -2^3 * 3 * 5 * 11 * 23 C2 x C2 x C2 x C6
-30660 -2^2 * 3 * 5 * 7 * 73 C2 x C2 x C2 x C6
-31620 -2^2 * 3 * 5 * 17 * 31 C2 x C2 x C2 x C6
-31908 -2^2 * 3 * 2659 C6 x C6
-32968 -2^3 * 13 * 317 C6 x C6
-33060 -2^2 * 3 * 5 * 19 * 29 C2 x C2 x C2 x C6
-34027 -7 * 4861 C3 x C6
-34507 -11 * 3137 C3 x C6
-34827 -3 * 13 * 19 * 47 C2 x C2 x C6
-34867 -7 * 17 * 293 C6 x C6
-34980 -2^2 * 3 * 5 * 11 * 53 C2 x C2 x C2 x C6
-35112 -2^3 * 3 * 7 * 11 * 19 C2 x C2 x C2 x C6
-36120 -2^3 * 3 * 5 * 7 * 43 C2 x C2 x C2 x C6
-36708 -2^2 * 3 * 7 * 19 * 23 C2 x C2 x C2 x C6
-37128 -2^3 * 3 * 7 * 13 * 17 C2 x C2 x C2 x C6
-37219 -7 * 13 * 409 C6 x C6
-37555 -5 * 7 * 29 * 37 C2 x C2 x C6
-38280 -2^3 * 3 * 5 * 11 * 29 C2 x C2 x C2 x C6
-39480 -2^3 * 3 * 5 * 7 * 47 C2 x C2 x C2 x C6
-39732 -2^2 * 3 * 7 * 11 * 43 C2 x C2 x C2 x C6
-40299 -3 * 7 * 19 * 101 C2 x C6 x C6
-40692 -2^2 * 3 * 3391 C6 x C6
-41412 -2^2 * 3 * 7 * 17 * 29 C2 x C2 x C2 x C6
-41860 -2^2 * 5 * 7 * 13 * 23 C2 x C2 x C2 x C6
-42315 -3 * 5 * 7 * 13 * 31 C2 x C2 x C2 x C6
-42427 -7 * 11 * 19 * 29 C2 x C2 x C6
-42619 -17 * 23 * 109 C6 x C6
-43428 -2^2 * 3 * 7 * 11 * 47 C2 x C2 x C2 x C6
-43827 -3 * 7 * 2087 C6 x C6
-44004 -2^2 * 3 * 19 * 193 C2 x C6 x C6
-45220 -2^2 * 5 * 7 * 17 * 19 C2 x C2 x C2 x C6
-45835 -5 * 89 * 103 C6 x C6
-46587 -3 * 53 * 293 C6 x C6
-46740 -2^2 * 3 * 5 * 19 * 41 C2 x C2 x C2 x C6
-47355 -3 * 5 * 7 * 11 * 41 C2 x C2 x C2 x C6
-48052 -2^2 * 41 * 293 C6 x C6
-48472 -2^3 * 73 * 83 C6 x C6
-49128 -2^3 * 3 * 23 * 89 C2 x C6 x C6
-49812 -2^2 * 3 * 7 * 593 C2 x C6 x C6
-50388 -2^2 * 3 * 13 * 17 * 19 C2 x C2 x C2 x C6
-51051 -3 * 7 * 11 * 13 * 17 C2 x C2 x C2 x C6
-51348 -2^2 * 3 * 11 * 389 C2 x C6 x C6
-52360 -2^3 * 5 * 7 * 11 * 17 C2 x C2 x C2 x C6
-54195 -3 * 5 * 3613 C6 x C6
-58920 -2^3 * 3 * 5 * 491 C2 x C6 x C6
-60099 -3 * 13 * 23 * 67 C2 x C6 x C6
-63492 -2^2 * 3 * 11 * 13 * 37 C2 x C2 x C2 x C6
-64155 -3 * 5 * 7 * 13 * 47 C2 x C2 x C2 x C6
-67480 -2^3 * 5 * 7 * 241 C2 x C6 x C6
-70035 -3 * 5 * 7 * 23 * 29 C2 x C2 x C2 x C6
-72435 -3 * 5 * 11 * 439 C2 x C6 x C6
-78180 -2^2 * 3 * 5 * 1303 C2 x C6 x C6
-78708 -2^2 * 3 * 7 * 937 C2 x C6 x C6
-81867 -3 * 29 * 941 C6 x C6
-83395 -5 * 13 * 1283 C6 x C6
-84072 -2^3 * 3 * 31 * 113 C2 x C6 x C6
-86955 -3 * 5 * 11 * 17 * 31 C2 x C2 x C2 x C6
-87720 -2^3 * 3 * 5 * 17 * 43 C2 x C2 x C6 x C6
-87780 -2^2 * 3 * 5 * 7 * 11 * 19 C2 x C2 x C2 x C2 x C6
-92827 -7 * 89 * 149 C6 x C6
-94395 -3 * 5 * 7 * 29 * 31 C2 x C2 x C2 x C6
-95448 -2^3 * 3 * 41 * 97 C2 x C6 x C6
-100488 -2^3 * 3 * 53 * 79 C2 x C6 x C6
-106260 -2^2 * 3 * 5 * 7 * 11 * 23 C2 x C2 x C2 x C2 x C6
-107848 -2^3 * 13 * 17 * 61 C2 x C6 x C6
-112795 -5 * 17 * 1327 C6 x C6
-115780 -2^2 * 5 * 7 * 827 C2 x C6 x C6
-116083 -11 * 61 * 173 C6 x C6
-117480 -2^3 * 3 * 5 * 11 * 89 C2 x C2 x C6 x C6
-119112 -2^3 * 3 * 7 * 709 C2 x C6 x C6
-121720 -2^3 * 5 * 17 * 179 C2 x C6 x C6
-125652 -2^2 * 3 * 37 * 283 C2 x C6 x C6
-132328 -2^3 * 7 * 17 * 139 C2 x C6 x C6
-137067 -3 * 7 * 61 * 107 C2 x C6 x C6
-138468 -2^2 * 3 * 11 * 1049 C2 x C6 x C6
-145860 -2^2 * 3 * 5 * 11 * 13 * 17 C2 x C2 x C2 x C2 x C6
-148852 -2^2 * 11 * 17 * 199 C2 x C6 x C6
-152355 -3 * 5 * 7 * 1451 C2 x C6 x C6
-154212 -2^2 * 3 * 71 * 181 C2 x C6 x C6
-180840 -2^3 * 3 * 5 * 11 * 137 C2 x C2 x C6 x C6
-183012 -2^2 * 3 * 101 * 151 C2 x C6 x C6
-183768 -2^3 * 3 * 13 * 19 * 31 C2 x C2 x C6 x C6
-192003 -3 * 7 * 41 * 223 C2 x C6 x C6
-195960 -2^3 * 3 * 5 * 23 * 71 C2 x C2 x C6 x C6
-198795 -3 * 5 * 29 * 457 C2 x C6 x C6
-199348 -2^2 * 19 * 43 * 61 C2 x C6 x C6
-204568 -2^3 * 7 * 13 * 281 C2 x C6 x C6
-211432 -2^3 * 13 * 19 * 107 C2 x C6 x C6
-214008 -2^3 * 3 * 37 * 241 C2 x C6 x C6
-224580 -2^2 * 3 * 5 * 19 * 197 C2 x C2 x C6 x C6
-231240 -2^3 * 3 * 5 * 41 * 47 C2 x C2 x C6 x C6
-287155 -5 * 11 * 23 * 227 C2 x C6 x C6
-303160 -2^3 * 5 * 11 * 13 * 53 C2 x C2 x C6 x C6
-315723 -3 * 19 * 29 * 191 C2 x C6 x C6
-341715 -3 * 5 * 11 * 19 * 109 C2 x C2 x C6 x C6
-343380 -2^2 * 3 * 5 * 59 * 97 C2 x C2 x C6 x C6
-352968 -2^3 * 3 * 7 * 11 * 191 C2 x C2 x C6 x C6
-393108 -2^2 * 3 * 17 * 41 * 47 C2 x C2 x C6 x C6
-394420 -2^2 * 5 * 13 * 37 * 41 C2 x C2 x C6 x C6
-397155 -3 * 5 * 11 * 29 * 83 C2 x C2 x C6 x C6
-404547 -3 * 11 * 13 * 23 * 41 C2 x C2 x C6 x C6
-419640 -2^3 * 3 * 5 * 13 * 269 C2 x C2 x C6 x C6
-423640 -2^3 * 5 * 7 * 17 * 89 C2 x C2 x C6 x C6
-453435 -3 * 5 * 19 * 37 * 43 C2 x C2 x C6 x C6
-458920 -2^3 * 5 * 7 * 11 * 149 C2 x C2 x C6 x C6
-507892 -2^2 * 7 * 11 * 17 * 97 C2 x C2 x C6 x C6
-512715 -3 * 5 * 7 * 19 * 257 C2 x C2 x C6 x C6
-522795 -3 * 5 * 7 * 13 * 383 C2 x C2 x C6 x C6
-603460 -2^2 * 5 * 11 * 13 * 211 C2 x C2 x C6 x C6
-668980 -2^2 * 5 * 13 * 31 * 83 C2 x C2 x C6 x C6
-680043 -3 * 7 * 13 * 47 * 53 C2 x C2 x C6 x C6
-697620 -2^2 * 3 * 5 * 7 * 11 * 151 C2 x C2 x C2 x C6 x C6
-740355 -3 * 5 * 7 * 11 * 641 C2 x C2 x C6 x C6
-740532 -2^2 * 3 * 13 * 47 * 101 C2 x C2 x C6 x C6
-742980 -2^2 * 3 * 5 * 7 * 29 * 61 C2 x C2 x C2 x C6 x C6
-820120 -2^3 * 5 * 7 * 29 * 101 C2 x C2 x C6 x C6
-899283 -3 * 7 * 11 * 17 * 229 C2 x C2 x C6 x C6
-941640 -2^3 * 3 * 5 * 7 * 19 * 59 C2 x C2 x C2 x C6 x C6
-1162392 -2^3 * 3 * 7 * 11 * 17 * 37 C2 x C2 x C2 x C6 x C6
-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

The following table is only complete up to discriminant 3.1*10^20.

Discriminant Factorization Class group
-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

The following table is complete assuming that there are no Siegel zeros. Without any assumption there might be one missing field. 

Discriminant Factorization Class group
-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
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-76755 -3 * 5 * 7 * 17 * 43 C2 x C2 x C2 x C8
-76843 -13 * 23 * 257 C4 x C8
-77140 -2^2 * 5 * 7 * 19 * 29 C2 x C2 x C2 x C8
-77995 -5 * 19 * 821 C4 x C8
-79048 -2^3 * 41 * 241 C8 x C8
-80067 -3 * 13 * 2053 C4 x C8
-80808 -2^3 * 3 * 7 * 13 * 37 C2 x C2 x C2 x C8
-80835 -3 * 5 * 17 * 317 C2 x C4 x C8
-81403 -7 * 29 * 401 C4 x C8
-81592 -2^3 * 7 * 31 * 47 C2 x C4 x C8
-81780 -2^2 * 3 * 5 * 29 * 47 C2 x C2 x C4 x C8
-82212 -2^2 * 3 * 13 * 17 * 31 C2 x C2 x C2 x C8
-82632 -2^3 * 3 * 11 * 313 C2 x C4 x C8
-83028 -2^2 * 3 * 11 * 17 * 37 C2 x C2 x C2 x C8
-83220 -2^2 * 3 * 5 * 19 * 73 C2 x C2 x C2 x C8
-84315 -3 * 5 * 7 * 11 * 73 C2 x C2 x C2 x C8
-84760 -2^3 * 5 * 13 * 163 C2 x C4 x C8
-85195 -5 * 11 * 1549 C8 x C8
-85540 -2^2 * 5 * 7 * 13 * 47 C2 x C2 x C2 x C8
-86020 -2^2 * 5 * 11 * 17 * 23 C2 x C2 x C2 x C8
-87283 -7 * 37 * 337 C4 x C8
-89284 -2^2 * 13 * 17 * 101 C2 x C8 x C8
-89355 -3 * 5 * 7 * 23 * 37 C2 x C2 x C2 x C8
-89947 -11 * 13 * 17 * 37 C2 x C2 x C8
-90948 -2^2 * 3 * 11 * 13 * 53 C2 x C2 x C2 x C8
-92235 -3 * 5 * 11 * 13 * 43 C2 x C2 x C2 x C8
-92820 -2^2 * 3 * 5 * 7 * 13 * 17 C2 x C2 x C2 x C2 x C8
-93940 -2^2 * 5 * 7 * 11 * 61 C2 x C2 x C2 x C8
-94963 -11 * 89 * 97 C4 x C8
-95640 -2^3 * 3 * 5 * 797 C2 x C8 x C8
-95880 -2^3 * 3 * 5 * 17 * 47 C2 x C2 x C2 x C8
-95979 -3 * 13 * 23 * 107 C2 x C4 x C8
-96915 -3 * 5 * 7 * 13 * 71 C2 x C2 x C2 x C8
-98427 -3 * 7 * 43 * 109 C2 x C4 x C8
-99528 -2^3 * 3 * 11 * 13 * 29 C2 x C2 x C2 x C8
-100104 -2^3 * 3 * 43 * 97 C2 x C8 x C8
-100195 -5 * 29 * 691 C8 x C8
-100947 -3 * 7 * 11 * 19 * 23 C2 x C2 x C2 x C8
-101752 -2^3 * 7 * 23 * 79 C2 x C4 x C8
-102795 -3 * 5 * 7 * 11 * 89 C2 x C2 x C2 x C8
-104052 -2^2 * 3 * 13 * 23 * 29 C2 x C2 x C2 x C8
-104091 -3 * 13 * 17 * 157 C2 x C4 x C8
-104403 -3 * 13 * 2677 C8 x C8
-104980 -2^2 * 5 * 29 * 181 C2 x C4 x C8
-106536 -2^3 * 3 * 23 * 193 C2 x C8 x C8
-108003 -3 * 7 * 37 * 139 C2 x C4 x C8
-108915 -3 * 5 * 53 * 137 C2 x C4 x C8
-110523 -3 * 7 * 19 * 277 C2 x C4 x C8
-110635 -5 * 7 * 29 * 109 C2 x C4 x C8
-111112 -2^3 * 17 * 19 * 43 C2 x C4 x C8
-112035 -3 * 5 * 7 * 11 * 97 C2 x C2 x C2 x C8
-112884 -2^2 * 3 * 23 * 409 C2 x C8 x C8
-112980 -2^2 * 3 * 5 * 7 * 269 C2 x C2 x C4 x C8
-113883 -3 * 7 * 11 * 17 * 29 C2 x C2 x C2 x C8
-116932 -2^2 * 23 * 31 * 41 C2 x C4 x C8
-117028 -2^2 * 17 * 1721 C8 x C8
-117096 -2^3 * 3 * 7 * 17 * 41 C2 x C2 x C4 x C8
-117507 -3 * 13 * 23 * 131 C2 x C4 x C8
-119595 -3 * 5 * 7 * 17 * 67 C2 x C2 x C2 x C8
-120120 -2^3 * 3 * 5 * 7 * 11 * 13 C2 x C2 x C2 x C2 x C8
-121560 -2^3 * 3 * 5 * 1013 C2 x C8 x C8
-123123 -3 * 7 * 11 * 13 * 41 C2 x C2 x C2 x C8
-123508 -2^2 * 7 * 11 * 401 C2 x C4 x C8
-124392 -2^3 * 3 * 71 * 73 C2 x C4 x C8
-124683 -3 * 13 * 23 * 139 C2 x C4 x C8
-125643 -3 * 7 * 31 * 193 C2 x C4 x C8
-126555 -3 * 5 * 11 * 13 * 59 C2 x C2 x C2 x C8
-128472 -2^3 * 3 * 53 * 101 C2 x C4 x C8
-128632 -2^3 * 7 * 2297 C8 x C8
-130515 -3 * 5 * 7 * 11 * 113 C2 x C2 x C2 x C8
-131560 -2^3 * 5 * 11 * 13 * 23 C2 x C2 x C2 x C8
-132483 -3 * 13 * 43 * 79 C2 x C4 x C8
-133315 -5 * 7 * 13 * 293 C2 x C4 x C8
-138292 -2^2 * 7 * 11 * 449 C2 x C4 x C8
-139780 -2^2 * 5 * 29 * 241 C2 x C4 x C8
-139867 -7 * 13 * 29 * 53 C2 x C4 x C8
-140595 -3 * 5 * 7 * 13 * 103 C2 x C2 x C2 x C8
-143115 -3 * 5 * 7 * 29 * 47 C2 x C2 x C2 x C8
-143220 -2^2 * 3 * 5 * 7 * 11 * 31 C2 x C2 x C2 x C2 x C8
-147940 -2^2 * 5 * 13 * 569 C2 x C4 x C8
-150052 -2^2 * 7 * 23 * 233 C2 x C4 x C8
-152395 -5 * 29 * 1051 C8 x C8
-155155 -5 * 7 * 11 * 13 * 31 C2 x C2 x C2 x C8
-157080 -2^3 * 3 * 5 * 7 * 11 * 17 C2 x C2 x C2 x C2 x C8
-157795 -5 * 11 * 19 * 151 C2 x C4 x C8
-159960 -2^3 * 3 * 5 * 31 * 43 C2 x C2 x C4 x C8
-160563 -3 * 13 * 23 * 179 C2 x C4 x C8
-163947 -3 * 7 * 37 * 211 C2 x C4 x C8
-172635 -3 * 5 * 17 * 677 C2 x C4 x C8
-173128 -2^3 * 17 * 19 * 67 C2 x C4 x C8
-173667 -3 * 13 * 61 * 73 C2 x C4 x C8
-173755 -5 * 19 * 31 * 59 C2 x C4 x C8
-175483 -7 * 11 * 43 * 53 C2 x C4 x C8
-175560 -2^3 * 3 * 5 * 7 * 11 * 19 C2 x C2 x C2 x C2 x C8
-175960 -2^3 * 5 * 53 * 83 C2 x C4 x C8
-183540 -2^2 * 3 * 5 * 7 * 19 * 23 C2 x C2 x C2 x C2 x C8
-184008 -2^3 * 3 * 11 * 17 * 41 C2 x C2 x C4 x C8
-185235 -3 * 5 * 53 * 233 C2 x C4 x C8
-185640 -2^3 * 3 * 5 * 7 * 13 * 17 C2 x C2 x C2 x C2 x C8
-186235 -5 * 7 * 17 * 313 C2 x C4 x C8
-187224 -2^3 * 3 * 29 * 269 C2 x C8 x C8
-189267 -3 * 13 * 23 * 211 C2 x C4 x C8
-189987 -3 * 7 * 83 * 109 C2 x C4 x C8
-193323 -3 * 13 * 4957 C8 x C8
-193620 -2^2 * 3 * 5 * 7 * 461 C2 x C2 x C4 x C8
-196168 -2^3 * 7 * 31 * 113 C2 x C4 x C8
-198835 -5 * 7 * 13 * 19 * 23 C2 x C2 x C2 x C8
-199563 -3 * 7 * 13 * 17 * 43 C2 x C2 x C2 x C8
-199795 -5 * 31 * 1289 C8 x C8
-205620 -2^2 * 3 * 5 * 23 * 149 C2 x C2 x C4 x C8
-207955 -5 * 11 * 19 * 199 C2 x C4 x C8
-209352 -2^3 * 3 * 11 * 13 * 61 C2 x C2 x C4 x C8
-212520 -2^3 * 3 * 5 * 7 * 11 * 23 C2 x C2 x C2 x C2 x C8
-212667 -3 * 7 * 13 * 19 * 41 C2 x C2 x C2 x C8
-213060 -2^2 * 3 * 5 * 53 * 67 C2 x C2 x C4 x C8
-213780 -2^2 * 3 * 5 * 7 * 509 C2 x C2 x C4 x C8
-218395 -5 * 31 * 1409 C8 x C8
-219219 -3 * 7 * 11 * 13 * 73 C2 x C2 x C4 x C8
-220915 -5 * 17 * 23 * 113 C2 x C4 x C8
-220980 -2^2 * 3 * 5 * 29 * 127 C2 x C2 x C4 x C8
-221995 -5 * 29 * 1531 C8 x C8
-227032 -2^3 * 13 * 37 * 59 C2 x C4 x C8
-230280 -2^3 * 3 * 5 * 19 * 101 C2 x C2 x C4 x C8
-230395 -5 * 11 * 59 * 71 C2 x C4 x C8
-230763 -3 * 13 * 61 * 97 C2 x C4 x C8
-232932 -2^2 * 3 * 7 * 47 * 59 C2 x C2 x C4 x C8
-236467 -7 * 11 * 37 * 83 C2 x C4 x C8
-237595 -5 * 19 * 41 * 61 C2 x C4 x C8
-243507 -3 * 11 * 47 * 157 C2 x C8 x C8
-244920 -2^3 * 3 * 5 * 13 * 157 C2 x C2 x C4 x C8
-247080 -2^3 * 3 * 5 * 29 * 71 C2 x C2 x C4 x C8
-253995 -3 * 5 * 7 * 41 * 59 C2 x C2 x C4 x C8
-257748 -2^2 * 3 * 47 * 457 C2 x C8 x C8
-259435 -5 * 11 * 53 * 89 C2 x C4 x C8
-263112 -2^3 * 3 * 19 * 577 C2 x C8 x C8
-265560 -2^3 * 3 * 5 * 2213 C2 x C8 x C8
-266532 -2^2 * 3 * 7 * 19 * 167 C2 x C2 x C4 x C8
-272283 -3 * 11 * 37 * 223 C2 x C4 x C8
-275352 -2^3 * 3 * 7 * 11 * 149 C2 x C2 x C4 x C8
-280635 -3 * 5 * 53 * 353 C2 x C8 x C8
-283195 -5 * 11 * 19 * 271 C2 x C8 x C8
-286180 -2^2 * 5 * 41 * 349 C2 x C8 x C8
-289912 -2^3 * 7 * 31 * 167 C2 x C8 x C8
-296835 -3 * 5 * 7 * 11 * 257 C2 x C2 x C4 x C8
-298452 -2^2 * 3 * 7 * 11 * 17 * 19 C2 x C2 x C2 x C2 x C8
-304152 -2^3 * 3 * 19 * 23 * 29 C2 x C2 x C4 x C8
-304612 -2^2 * 7 * 11 * 23 * 43 C2 x C2 x C4 x C8
-304843 -7 * 11 * 37 * 107 C2 x C4 x C8
-304980 -2^2 * 3 * 5 * 13 * 17 * 23 C2 x C2 x C2 x C2 x C8
-308760 -2^3 * 3 * 5 * 31 * 83 C2 x C2 x C4 x C8
-319515 -3 * 5 * 7 * 17 * 179 C2 x C2 x C4 x C8
-320307 -3 * 13 * 43 * 191 C2 x C4 x C8
-321123 -3 * 11 * 37 * 263 C2 x C8 x C8
-321763 -13 * 53 * 467 C8 x C8
-323323 -7 * 11 * 13 * 17 * 19 C2 x C2 x C2 x C8
-337755 -3 * 5 * 11 * 23 * 89 C2 x C2 x C4 x C8
-340195 -5 * 19 * 3581 C8 x C8
-353860 -2^2 * 5 * 13 * 1361 C2 x C8 x C8
-357627 -3 * 23 * 71 * 73 C2 x C8 x C8
-361284 -2^2 * 3 * 7 * 11 * 17 * 23 C2 x C2 x C2 x C4 x C8
-366360 -2^3 * 3 * 5 * 43 * 71 C2 x C2 x C4 x C8
-366760 -2^3 * 5 * 53 * 173 C2 x C8 x C8
-369835 -5 * 17 * 19 * 229 C2 x C4 x C8
-374088 -2^3 * 3 * 11 * 13 * 109 C2 x C2 x C4 x C8
-374595 -3 * 5 * 13 * 17 * 113 C2 x C2 x C4 x C8
-383380 -2^2 * 5 * 29 * 661 C2 x C8 x C8
-385795 -5 * 19 * 31 * 131 C2 x C4 x C8
-386628 -2^2 * 3 * 11 * 29 * 101 C2 x C2 x C4 x C8
-409960 -2^3 * 5 * 37 * 277 C2 x C8 x C8
-417435 -3 * 5 * 17 * 1637 C2 x C8 x C8
-428835 -3 * 5 * 11 * 23 * 113 C2 x C2 x C4 x C8
-433540 -2^2 * 5 * 53 * 409 C2 x C8 x C8
-443667 -3 * 7 * 37 * 571 C2 x C8 x C8
-448035 -3 * 5 * 7 * 17 * 251 C2 x C2 x C4 x C8
-457620 -2^2 * 3 * 5 * 29 * 263 C2 x C2 x C4 x C8
-474628 -2^2 * 7 * 11 * 23 * 67 C2 x C2 x C4 x C8
-480907 -7 * 23 * 29 * 103 C2 x C4 x C8
-488523 -3 * 7 * 43 * 541 C2 x C8 x C8
-489787 -17 * 47 * 613 C8 x C8
-492388 -2^2 * 13 * 17 * 557 C2 x C8 x C8
-502660 -2^2 * 5 * 41 * 613 C2 x C8 x C8
-503659 -13 * 17 * 43 * 53 C4 x C4 x C8
-505960 -2^3 * 5 * 7 * 13 * 139 C2 x C2 x C4 x C8
-514228 -2^2 * 11 * 13 * 29 * 31 C2 x C2 x C4 x C8
-516243 -3 * 7 * 13 * 31 * 61 C2 x C2 x C4 x C8
-518635 -5 * 13 * 79 * 101 C2 x C8 x C8
-519915 -3 * 5 * 11 * 23 * 137 C2 x C2 x C4 x C8
-549915 -3 * 5 * 61 * 601 C2 x C8 x C8
-553540 -2^2 * 5 * 13 * 2129 C2 x C8 x C8
-557832 -2^3 * 3 * 11 * 2113 C2 x C8 x C8
-559083 -3 * 7 * 79 * 337 C2 x C8 x C8
-563640 -2^3 * 3 * 5 * 7 * 11 * 61 C2 x C2 x C2 x C4 x C8
-563955 -3 * 5 * 7 * 41 * 131 C2 x C2 x C4 x C8
-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
-703560 -2^3 * 3 * 5 * 11 * 13 * 41 C2 x C2 x C2 x C4 x C8
-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
-857220 -2^2 * 3 * 5 * 7 * 13 * 157 C2 x C2 x C2 x C4 x C8
-876315 -3 * 5 * 11 * 47 * 113 C2 x C2 x C8 x C8
-876435 -3 * 5 * 7 * 17 * 491 C2 x C2 x C8 x C8
-894660 -2^2 * 3 * 5 * 13 * 31 * 37 C2 x C2 x C2 x C4 x C8
-937560 -2^3 * 3 * 5 * 13 * 601 C2 x C2 x C8 x C8
-959803 -13 * 17 * 43 * 101 C4 x C4 x C8
-963235 -5 * 7 * 13 * 29 * 73 C2 x C2 x C4 x C8
-980148 -2^2 * 3 * 13 * 61 * 103 C2 x C2 x C8 x C8
-990964 -2^2 * 13 * 17 * 19 * 59 C2 x C2 x C8 x C8
-1039795 -5 * 29 * 71 * 101 C2 x C8 x C8
-1065540 -2^2 * 3 * 5 * 7 * 43 * 59 C2 x C2 x C2 x C4 x C8
-1076712 -2^3 * 3 * 7 * 13 * 17 * 29 C2 x C2 x C2 x C4 x C8
-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
-1278552 -2^3 * 3 * 11 * 29 * 167 C2 x C2 x C8 x C8
-1291620 -2^2 * 3 * 5 * 11 * 19 * 103 C2 x C2 x C2 x C4 x C8
-1307523 -3 * 7 * 19 * 29 * 113 C2 x C2 x C8 x C8
-1362760 -2^3 * 5 * 7 * 31 * 157 C2 x C2 x C8 x C8
-1364808 -2^3 * 3 * 19 * 41 * 73 C2 x C2 x C8 x C8
-1368840 -2^3 * 3 * 5 * 11 * 17 * 61 C2 x C2 x C2 x C4 x C8
-1390180 -2^2 * 5 * 11 * 71 * 89 C2 x C2 x C8 x C8
-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
-1490952 -2^3 * 3 * 23 * 37 * 73 C2 x C2 x C8 x C8
-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
-1567720 -2^3 * 5 * 7 * 11 * 509 C2 x C2 x C8 x C8
-1592115 -3 * 5 * 7 * 59 * 257 C2 x C2 x C8 x C8
-1707288 -2^3 * 3 * 11 * 29 * 223 C2 x C2 x C8 x C8
-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
-2104707 -3 * 11 * 23 * 47 * 59 C2 x C2 x C8 x C8
-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
-2229123 -3 * 13 * 61 * 937 C4 x C8 x C8
-2309307 -3 * 7 * 11 * 13 * 769 C2 x C2 x C8 x C8
-2345595 -3 * 5 * 7 * 89 * 251 C2 x C2 x C8 x C8
-2376660 -2^2 * 3 * 5 * 11 * 13 * 277 C2 x C2 x C2 x C8 x C8
-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
C-Programs

The following two c-programs can be used to compute all imaginary quadratic number fields with exponent less or equal to 8 and discriminant bound 3.1·1020.

Smallest Split fixed.c 

No small split.c

List of fields

Julia Programs

The following file contains the Julia code. You need to install Julia including the Hecke and the Markdown package. The function M1 computes the imginary quadratic number fields of given exponent. The functions M2a, M2b, M3a, and M3b compute the corresponding families.

Download File