An Igusa CM invariant is specified by a sequence of three polynomials
[ H1(x), G2(x)/N2, G3(x)/N3],
such that
H1(x), G2(x), and G3(x) are in Z[x],
H1(i1) = 0, |
i2 = G2(i1)/N1N2, |
i3 = G3(i1)/N1N3, |
where N1 = H1'(i1),
and N2 and N3 are integers, and
i1 = I4I6/I10, |
i2 = I23I4/I10, |
i3 = I22I6/I10,
|
in terms of the Igusa-Clebsch invariants
[
I2,
I4,
I6,
I10
].
Degree:
[Non-normal]
[Cyclic]
Degree 90 Igusa CM invariants of non-normal (D4) fields: 89
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 97, 2273] |
[1] |
1 |
[317, 97, 2273] |
45 |
C3 x C15 |
2) |
[157, 173, 7129] |
[1] |
1 |
[157, 173, 7129] |
45 |
C45 |
3) |
[157, 153, 3929] |
[1] |
1 |
[157, 153, 3929] |
45 |
C45 |
4) |
[229, 137, 4177] |
[1] |
1 |
[229, 137, 4177] |
135 |
C3 x C45 |
5) |
[1049, 870, 122089] |
[1] |
1 |
[1049, 870, 122089] |
45 |
C3 x C15 |
6) |
[109, 250, 11701] |
[1] |
1 |
[109, 250, 11701] |
45 |
C45 |
7) |
[733, 222, 593] |
[1] |
1 |
[733, 222, 593] |
135 |
C3 x C45 |
8) |
[13, 1790, 379825] |
[1] |
2 |
[13, 1790, 379825] |
90 |
C90 |
9) |
[13, 809, 142297] |
[1] |
1 |
[13, 809, 142297] |
45 |
C45 |
10) |
[13, 457, 16381] |
[1] |
1 |
[13, 457, 16381] |
45 |
C45 |
11) |
[13, 653, 91129] |
[1] |
1 |
[13, 653, 91129] |
45 |
C45 |
12) |
[8, 1042, 269641] |
[1] |
1 |
[8, 1042, 269641] |
45 |
C45 |
13) |
[8, 1158, 289033] |
[1] |
1 |
[8, 1158, 289033] |
45 |
C45 |
14) |
[8, 394, 37657] |
[1] |
2 |
[8, 394, 37657] |
90 |
C90 |
15) |
[8, 350, 26017] |
[1] |
1 |
[8, 350, 26017] |
45 |
C45 |
16) |
[8, 666, 95401] |
[1] |
2 |
[8, 666, 95401] |
90 |
C90 |
17) |
[8, 822, 101209] |
[1] |
1 |
[8, 822, 101209] |
45 |
C45 |
18) |
[8, 858, 182473] |
[1] |
2 |
[8, 858, 182473] |
90 |
C3 x C30 |
19) |
[8, 1350, 369097] |
[1] |
1 |
[8, 1350, 369097] |
45 |
C45 |
20) |
[8, 882, 190249] |
[1] |
1 |
[8, 882, 190249] |
45 |
C45 |
21) |
[8, 794, 155017] |
[1] |
2 |
[8, 794, 155017] |
90 |
C90 |
22) |
[8, 814, 121841] |
[1] |
2 |
[8, 814, 121841] |
90 |
C90 |
23) |
[8, 1238, 267961] |
[1] |
1 |
[8, 1238, 267961] |
45 |
C45 |
24) |
[5, 1141, 302009] |
[1] |
1 |
[5, 1141, 302009] |
45 |
C45 |
25) |
[5, 613, 92041] |
[1] |
1 |
[5, 613, 92041] |
45 |
C45 |
26) |
[5, 717, 117241] |
[1] |
1 |
[5, 717, 117241] |
45 |
C45 |
27) |
[5, 833, 145721] |
[1] |
1 |
[5, 833, 145721] |
45 |
C45 |
28) |
[5, 673, 111521] |
[1] |
1 |
[5, 673, 111521] |
45 |
C45 |
29) |
[5, 966, 225289] |
[1] |
1 |
[5, 966, 225289] |
45 |
C45 |
30) |
[5, 829, 160049] |
[1] |
1 |
[5, 829, 160049] |
45 |
C45 |
31) |
[5, 1021, 222329] |
[1] |
1 |
[5, 1021, 222329] |
45 |
C45 |
32) |
[5, 437, 47681] |
[1] |
1 |
[5, 437, 47681] |
45 |
C45 |
33) |
[5, 654, 91249] |
[1] |
1 |
[5, 654, 91249] |
45 |
C45 |
34) |
[5, 1026, 226189] |
[1] |
1 |
[5, 1026, 226189] |
45 |
C45 |
35) |
[5, 797, 138641] |
[1] |
1 |
[5, 797, 138641] |
45 |
C45 |
36) |
[5, 238, 14081] |
[2, 2] |
1 |
[5, 238, 14081] |
15 |
C15 |
37) |
[5, 1194, 300229] |
[1] |
1 |
[5, 1194, 300229] |
45 |
C45 |
38) |
[5, 817, 139861] |
[1] |
1 |
[5, 817, 139861] |
45 |
C45 |
39) |
[5, 1221, 363249] |
[1] |
2 |
[5, 1221, 363249] |
90 |
C90 |
40) |
[5, 569, 80929] |
[1] |
1 |
[5, 569, 80929] |
45 |
C45 |
41) |
[5, 158, 5521] |
[2, 2] |
1 |
[5, 158, 5521] |
15 |
C15 |
42) |
[5, 1689, 702369] |
[1] |
2 |
[5, 1689, 702369] |
90 |
C90 |
43) |
[5, 1001, 213949] |
[1] |
1 |
[5, 1001, 213949] |
45 |
C45 |
44) |
[5, 263, 16741] |
[1] |
2 |
[5, 263, 16741] |
90 |
C90 |
45) |
[5, 439, 47629] |
[1] |
2 |
[5, 439, 47629] |
90 |
C90 |
46) |
[5, 479, 57349] |
[1] |
2 |
[5, 479, 57349] |
90 |
C3 x C30 |
47) |
[5, 886, 164249] |
[1] |
1 |
[5, 886, 164249] |
45 |
C45 |
48) |
[5, 578, 81901] |
[1] |
1 |
[5, 578, 81901] |
45 |
C3 x C15 |
49) |
[5, 214, 11369] |
[2, 2] |
1 |
[5, 214, 11369] |
15 |
C15 |
50) |
[29, 236, 9748] |
[1] |
2 |
[29, 236, 9748] |
90 |
C90 |
51) |
[29, 477, 24337] |
[1] |
1 |
[29, 477, 24337] |
45 |
C45 |
52) |
[149, 141, 4933] |
[1] |
1 |
[149, 141, 4933] |
45 |
C45 |
53) |
[149, 186, 8053] |
[1] |
1 |
[149, 186, 8053] |
45 |
C45 |
54) |
[149, 180, 5716] |
[1] |
2 |
[149, 180, 5716] |
90 |
C90 |
55) |
[1877, 825, 757] |
[1] |
1 |
[1877, 825, 757] |
45 |
C45 |
56) |
[113, 918, 29881] |
[1] |
1 |
[113, 918, 29881] |
45 |
C45 |
57) |
[89, 807, 135556] |
[1] |
1 |
[89, 807, 135556] |
45 |
C45 |
58) |
[281, 791, 14164] |
[1] |
1 |
[281, 791, 14164] |
45 |
C45 |
59) |
[37, 174, 6977] |
[1] |
1 |
[37, 174, 6977] |
45 |
C45 |
60) |
[37, 150, 3257] |
[2, 2] |
1 |
[37, 150, 3257] |
15 |
C15 |
61) |
[37, 862, 156753] |
[1] |
1 |
[37, 862, 156753] |
45 |
C45 |
62) |
[5573, 141, 3577] |
[1] |
1 |
[5573, 141, 3577] |
45 |
C45 |
63) |
[61, 130, 2029] |
[1] |
1 |
[61, 130, 2029] |
45 |
C45 |
64) |
[197, 157, 6113] |
[1] |
1 |
[197, 157, 6113] |
45 |
C45 |
65) |
[17, 354, 27997] |
[1] |
1 |
[17, 354, 27997] |
45 |
C45 |
66) |
[17, 1086, 196657] |
[1] |
1 |
[17, 1086, 196657] |
45 |
C45 |
67) |
[17, 118, 3209] |
[1] |
1 |
[17, 118, 3209] |
45 |
C45 |
68) |
[17, 718, 126433] |
[1] |
1 |
[17, 718, 126433] |
45 |
C45 |
69) |
[17, 118, 3209] |
[2, 2] |
1 |
[17, 118, 3209] |
45 |
C45 |
70) |
[17, 1238, 295033] |
[1] |
1 |
[17, 1238, 295033] |
45 |
C45 |
71) |
[17, 1527, 582724] |
[1] |
1 |
[17, 1527, 582724] |
45 |
C45 |
72) |
[17, 1230, 299617] |
[1] |
1 |
[17, 1230, 299617] |
45 |
C3 x C15 |
73) |
[17, 1647, 660196] |
[1] |
1 |
[17, 1647, 660196] |
45 |
C45 |
74) |
[173, 145, 3137] |
[1] |
1 |
[173, 145, 3137] |
45 |
C45 |
75) |
[173, 222, 1249] |
[1] |
1 |
[173, 222, 1249] |
45 |
C45 |
76) |
[173, 789, 5077] |
[1] |
1 |
[173, 789, 5077] |
45 |
C3 x C15 |
77) |
[2909, 477, 38701] |
[1] |
1 |
[2909, 477, 38701] |
45 |
C45 |
78) |
[3041, 399, 2548] |
[1] |
2 |
[3041, 399, 2548] |
90 |
C90 |
79) |
[1013, 850, 144157] |
[1] |
1 |
[1013, 850, 144157] |
45 |
C45 |
80) |
[569, 394, 18325] |
[1] |
1 |
[569, 394, 18325] |
45 |
C45 |
81) |
[569, 975, 42916] |
[1] |
1 |
[569, 975, 42916] |
45 |
C45 |
82) |
[44, 380, 34516] |
[1] |
2 |
[44, 380, 34516] |
90 |
C90 |
83) |
[1004, 786, 129349] |
[1] |
2 |
[1004, 786, 129349] |
90 |
C3 x C30 |
84) |
[41, 1038, 79777] |
[1] |
1 |
[41, 1038, 79777] |
45 |
C45 |
85) |
[41, 1431, 511684] |
[1] |
1 |
[41, 1431, 511684] |
45 |
C3 x C15 |
86) |
[41, 1311, 417124] |
[1] |
1 |
[41, 1311, 417124] |
45 |
C45 |
87) |
[41, 1735, 748036] |
[1] |
1 |
[41, 1735, 748036] |
45 |
C45 |
88) |
[829, 497, 51597] |
[1] |
2 |
[829, 497, 51597] |
90 |
C90 |
89) |
[2633, 567, 724] |
[1] |
1 |
[2633, 567, 724] |
45 |
C45 |