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 126 Igusa CM invariants of non-normal (D4) fields: 49
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[853, 485, 10825] |
[1] |
2 |
[853, 485, 10825] |
126 |
C126 |
2) |
[797, 65, 857] |
[1] |
1 |
[797, 65, 857] |
63 |
C63 |
3) |
[821, 613, 93737] |
[1] |
1 |
[821, 613, 93737] |
63 |
C63 |
4) |
[13, 977, 238369] |
[1] |
1 |
[13, 977, 238369] |
63 |
C63 |
5) |
[13, 878, 125329] |
[1] |
1 |
[13, 878, 125329] |
63 |
C63 |
6) |
[13, 385, 12457] |
[1] |
1 |
[13, 385, 12457] |
63 |
C63 |
7) |
[13, 941, 219937] |
[1] |
1 |
[13, 941, 219937] |
63 |
C63 |
8) |
[13, 486, 45737] |
[1] |
1 |
[13, 486, 45737] |
63 |
C63 |
9) |
[13, 1205, 292777] |
[1] |
1 |
[13, 1205, 292777] |
63 |
C63 |
10) |
[8, 1666, 459961] |
[1] |
1 |
[8, 1666, 459961] |
63 |
C63 |
11) |
[8, 378, 34369] |
[1] |
1 |
[8, 378, 34369] |
63 |
C63 |
12) |
[8, 2070, 546937] |
[1] |
1 |
[8, 2070, 546937] |
63 |
C63 |
13) |
[5, 769, 130729] |
[1] |
1 |
[5, 769, 130729] |
63 |
C63 |
14) |
[5, 862, 185441] |
[1] |
1 |
[5, 862, 185441] |
63 |
C63 |
15) |
[5, 806, 150889] |
[1] |
1 |
[5, 806, 150889] |
63 |
C63 |
16) |
[5, 821, 168409] |
[1] |
1 |
[5, 821, 168409] |
63 |
C3 x C21 |
17) |
[5, 821, 164449] |
[1] |
1 |
[5, 821, 164449] |
63 |
C3 x C21 |
18) |
[5, 757, 142601] |
[1] |
1 |
[5, 757, 142601] |
63 |
C63 |
19) |
[5, 2409, 1349289] |
[1] |
2 |
[5, 2409, 1349289] |
126 |
C126 |
20) |
[5, 926, 213649] |
[1] |
1 |
[5, 926, 213649] |
63 |
C63 |
21) |
[5, 1617, 534321] |
[1] |
2 |
[5, 1617, 534321] |
126 |
C126 |
22) |
[5, 941, 220009] |
[1] |
1 |
[5, 941, 220009] |
63 |
C63 |
23) |
[5, 961, 230729] |
[1] |
1 |
[5, 961, 230729] |
63 |
C63 |
24) |
[5, 493, 52561] |
[1] |
1 |
[5, 493, 52561] |
63 |
C63 |
25) |
[5, 1317, 424161] |
[1] |
2 |
[5, 1317, 424161] |
126 |
C126 |
26) |
[5, 997, 248441] |
[1] |
1 |
[5, 997, 248441] |
63 |
C63 |
27) |
[5, 2829, 1607409] |
[1] |
2 |
[5, 2829, 1607409] |
126 |
C126 |
28) |
[5, 1097, 296201] |
[1] |
1 |
[5, 1097, 296201] |
63 |
C63 |
29) |
[5, 697, 114041] |
[1] |
1 |
[5, 697, 114041] |
63 |
C63 |
30) |
[5, 901, 202889] |
[1] |
1 |
[5, 901, 202889] |
63 |
C3 x C21 |
31) |
[5, 1021, 260609] |
[1] |
1 |
[5, 1021, 260609] |
63 |
C63 |
32) |
[5, 2569, 1477889] |
[1] |
2 |
[5, 2569, 1477889] |
126 |
C126 |
33) |
[5, 2086, 989849] |
[1] |
2 |
[5, 2086, 989849] |
126 |
C126 |
34) |
[5, 1518, 530001] |
[1] |
2 |
[5, 1518, 530001] |
126 |
C126 |
35) |
[29, 553, 21577] |
[1] |
1 |
[29, 553, 21577] |
63 |
C63 |
36) |
[29, 894, 195633] |
[1] |
2 |
[29, 894, 195633] |
126 |
C126 |
37) |
[29, 661, 109049] |
[1] |
1 |
[29, 661, 109049] |
63 |
C63 |
38) |
[29, 313, 24137] |
[1] |
1 |
[29, 313, 24137] |
63 |
C63 |
39) |
[29, 581, 43609] |
[1] |
1 |
[29, 581, 43609] |
63 |
C63 |
40) |
[941, 57, 577] |
[1] |
1 |
[941, 57, 577] |
63 |
C63 |
41) |
[1901, 73, 857] |
[1] |
1 |
[1901, 73, 857] |
189 |
C3 x C63 |
42) |
[53, 278, 11689] |
[1] |
1 |
[53, 278, 11689] |
63 |
C63 |
43) |
[37, 190, 3697] |
[1] |
1 |
[37, 190, 3697] |
63 |
C63 |
44) |
[61, 381, 17609] |
[1] |
1 |
[61, 381, 17609] |
63 |
C63 |
45) |
[773, 525, 25425] |
[1] |
4 |
[773, 525, 25425] |
252 |
C2 x C126 |
46) |
[181, 453, 7817] |
[1] |
1 |
[181, 453, 7817] |
63 |
C63 |
47) |
[389, 769, 136073] |
[1] |
1 |
[389, 769, 136073] |
63 |
C63 |
48) |
[41, 430, 4241] |
[1] |
1 |
[41, 430, 4241] |
63 |
C63 |
49) |
[101, 214, 9833] |
[1] |
1 |
[101, 214, 9833] |
63 |
C63 |