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 110 Igusa CM invariants of non-normal (D4) fields: 46
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[229, 129, 2729] |
[1] |
1 |
[229, 129, 2729] |
165 |
C165 |
2) |
[269, 121, 3593] |
[1] |
1 |
[269, 121, 3593] |
55 |
C55 |
3) |
[269, 706, 114925] |
[1] |
1 |
[269, 706, 114925] |
55 |
C55 |
4) |
[236, 270, 6661] |
[1] |
2 |
[236, 270, 6661] |
110 |
C110 |
5) |
[349, 81, 1553] |
[1] |
1 |
[349, 81, 1553] |
55 |
C55 |
6) |
[13, 193, 9049] |
[1] |
1 |
[13, 193, 9049] |
55 |
C55 |
7) |
[13, 394, 27109] |
[1] |
1 |
[13, 394, 27109] |
55 |
C55 |
8) |
[977, 738, 132253] |
[1] |
1 |
[977, 738, 132253] |
55 |
C55 |
9) |
[8, 1122, 242521] |
[1] |
1 |
[8, 1122, 242521] |
55 |
C55 |
10) |
[8, 870, 172297] |
[1] |
1 |
[8, 870, 172297] |
55 |
C55 |
11) |
[8, 790, 99577] |
[1] |
1 |
[8, 790, 99577] |
55 |
C55 |
12) |
[8, 1206, 352057] |
[1] |
1 |
[8, 1206, 352057] |
55 |
C55 |
13) |
[8, 1266, 342889] |
[1] |
1 |
[8, 1266, 342889] |
55 |
C55 |
14) |
[8, 1506, 519577] |
[1] |
1 |
[8, 1506, 519577] |
55 |
C55 |
15) |
[8, 506, 56809] |
[1] |
2 |
[8, 506, 56809] |
110 |
C110 |
16) |
[5, 1481, 531229] |
[1] |
1 |
[5, 1481, 531229] |
55 |
C55 |
17) |
[5, 1561, 572629] |
[1] |
1 |
[5, 1561, 572629] |
55 |
C55 |
18) |
[5, 929, 213229] |
[1] |
1 |
[5, 929, 213229] |
55 |
C55 |
19) |
[5, 713, 127081] |
[1] |
1 |
[5, 713, 127081] |
55 |
C55 |
20) |
[5, 1129, 271129] |
[1] |
1 |
[5, 1129, 271129] |
55 |
C55 |
21) |
[5, 1709, 716389] |
[1] |
1 |
[5, 1709, 716389] |
55 |
C55 |
22) |
[5, 1641, 673069] |
[1] |
1 |
[5, 1641, 673069] |
55 |
C55 |
23) |
[5, 1509, 530989] |
[1] |
1 |
[5, 1509, 530989] |
55 |
C55 |
24) |
[29, 271, 7333] |
[1] |
2 |
[29, 271, 7333] |
110 |
C110 |
25) |
[29, 1030, 60601] |
[1] |
1 |
[29, 1030, 60601] |
55 |
C55 |
26) |
[29, 437, 6961] |
[1] |
1 |
[29, 437, 6961] |
55 |
C55 |
27) |
[149, 669, 22453] |
[1] |
1 |
[149, 669, 22453] |
55 |
C55 |
28) |
[113, 990, 199825] |
[1] |
2 |
[113, 990, 199825] |
110 |
C110 |
29) |
[113, 878, 46273] |
[1] |
1 |
[113, 878, 46273] |
55 |
C55 |
30) |
[89, 1215, 338596] |
[1] |
1 |
[89, 1215, 338596] |
55 |
C55 |
31) |
[37, 326, 24201] |
[1] |
1 |
[37, 326, 24201] |
55 |
C55 |
32) |
[37, 237, 14033] |
[1] |
1 |
[37, 237, 14033] |
55 |
C55 |
33) |
[17, 214, 11177] |
[1] |
1 |
[17, 214, 11177] |
55 |
C55 |
34) |
[17, 1086, 288049] |
[1] |
1 |
[17, 1086, 288049] |
55 |
C55 |
35) |
[17, 214, 11177] |
[2, 2] |
1 |
[17, 214, 11177] |
55 |
C55 |
36) |
[17, 618, 30133] |
[1] |
1 |
[17, 618, 30133] |
55 |
C55 |
37) |
[17, 1022, 199921] |
[1] |
1 |
[17, 1022, 199921] |
55 |
C55 |
38) |
[1868, 706, 107797] |
[1] |
2 |
[1868, 706, 107797] |
110 |
C110 |
39) |
[181, 165, 6761] |
[1] |
1 |
[181, 165, 6761] |
55 |
C55 |
40) |
[44, 366, 31333] |
[1] |
2 |
[44, 366, 31333] |
110 |
C110 |
41) |
[73, 607, 44644] |
[1] |
1 |
[73, 607, 44644] |
55 |
C55 |
42) |
[41, 1503, 556132] |
[1] |
1 |
[41, 1503, 556132] |
55 |
C55 |
43) |
[41, 306, 15373] |
[1] |
1 |
[41, 306, 15373] |
55 |
C55 |
44) |
[41, 855, 97876] |
[1] |
1 |
[41, 855, 97876] |
55 |
C55 |
45) |
[397, 413, 6813] |
[1] |
1 |
[397, 413, 6813] |
55 |
C55 |
46) |
[101, 621, 20029] |
[1] |
1 |
[101, 621, 20029] |
55 |
C55 |