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 208 Igusa CM invariants of non-normal (D4) fields: 37
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1717, 1173, 219929] |
[1] |
1 |
[1717, 1173, 219929] |
208 |
C2 x C104 |
2) |
[317, 597, 54153] |
[1] |
2 |
[317, 597, 54153] |
208 |
C2 x C104 |
3) |
[661, 1717, 736857] |
[1] |
1 |
[661, 1717, 736857] |
104 |
C104 |
4) |
[236, 402, 25297] |
[1] |
1 |
[236, 402, 25297] |
104 |
C2 x C52 |
5) |
[88, 250, 14833] |
[1] |
1 |
[88, 250, 14833] |
104 |
C2 x C52 |
6) |
[97, 886, 8457] |
[1] |
1 |
[97, 886, 8457] |
104 |
C104 |
7) |
[985, 151, 3484] |
[1] |
1 |
[985, 151, 3484] |
624 |
C4 x C156 |
8) |
[913, 187, 6688] |
[1] |
1 |
[913, 187, 6688] |
104 |
C2 x C52 |
9) |
[517, 1089, 280841] |
[1] |
1 |
[517, 1089, 280841] |
104 |
C2 x C52 |
10) |
[13, 115, 3043] |
[1] |
1 |
[13, 115, 3043] |
104 |
C2 x C52 |
11) |
[5, 837, 165241] |
[1] |
1 |
[5, 837, 165241] |
104 |
C104 |
12) |
[5, 1481, 536089] |
[1] |
1 |
[5, 1481, 536089] |
104 |
C104 |
13) |
[5, 1721, 723929] |
[1] |
1 |
[5, 1721, 723929] |
104 |
C104 |
14) |
[5, 1766, 771689] |
[1] |
1 |
[5, 1766, 771689] |
104 |
C104 |
15) |
[29, 582, 84217] |
[1] |
1 |
[29, 582, 84217] |
104 |
C2 x C52 |
16) |
[92, 570, 79753] |
[1] |
1 |
[92, 570, 79753] |
104 |
C104 |
17) |
[2501, 713, 21425] |
[1] |
1 |
[2501, 713, 21425] |
416 |
C2 x C208 |
18) |
[1093, 1237, 237993] |
[1] |
1 |
[1093, 1237, 237993] |
520 |
C520 |
19) |
[1453, 1309, 419289] |
[1] |
1 |
[1453, 1309, 419289] |
104 |
C104 |
20) |
[248, 474, 49969] |
[1] |
1 |
[248, 474, 49969] |
104 |
C104 |
21) |
[248, 426, 33217] |
[1] |
1 |
[248, 426, 33217] |
104 |
C104 |
22) |
[185, 551, 75484] |
[1] |
1 |
[185, 551, 75484] |
208 |
C4 x C52 |
23) |
[305, 483, 56416] |
[1] |
1 |
[305, 483, 56416] |
208 |
C4 x C52 |
24) |
[28, 574, 81361] |
[1] |
1 |
[28, 574, 81361] |
104 |
C2 x C52 |
25) |
[197, 437, 36661] |
[1] |
1 |
[197, 437, 36661] |
104 |
C104 |
26) |
[965, 161, 4309] |
[1] |
1 |
[965, 161, 4309] |
208 |
C2 x C2 x C52 |
27) |
[1061, 117, 3157] |
[1] |
1 |
[1061, 117, 3157] |
104 |
C2 x C52 |
28) |
[668, 282, 9193] |
[1] |
1 |
[668, 282, 9193] |
104 |
C104 |
29) |
[77, 497, 57421] |
[1] |
1 |
[77, 497, 57421] |
104 |
C2 x C52 |
30) |
[653, 309, 19789] |
[1] |
1 |
[653, 309, 19789] |
104 |
C2 x C52 |
31) |
[73, 662, 14953] |
[1] |
1 |
[73, 662, 14953] |
104 |
C104 |
32) |
[73, 155, 5988] |
[1] |
1 |
[73, 155, 5988] |
104 |
C104 |
33) |
[73, 319, 25276] |
[1] |
1 |
[73, 319, 25276] |
104 |
C2 x C52 |
34) |
[73, 667, 34116] |
[1] |
1 |
[73, 667, 34116] |
104 |
C104 |
35) |
[101, 537, 69037] |
[1] |
1 |
[101, 537, 69037] |
104 |
C2 x C52 |
36) |
[101, 417, 34357] |
[1] |
1 |
[101, 417, 34357] |
104 |
C2 x C52 |
37) |
[1949, 1033, 227305] |
[1] |
1 |
[1949, 1033, 227305] |
104 |
C104 |