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 220 Igusa CM invariants of non-normal (D4) fields: 56
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[809, 1119, 142948] |
[1] |
1 |
[809, 1119, 142948] |
110 |
C110 |
2) |
[237, 133, 3889] |
[1] |
1 |
[237, 133, 3889] |
110 |
C110 |
3) |
[376, 250, 12241] |
[1] |
1 |
[376, 250, 12241] |
110 |
C110 |
4) |
[129, 814, 64513] |
[1] |
1 |
[129, 814, 64513] |
110 |
C110 |
5) |
[104, 1010, 209161] |
[1] |
1 |
[104, 1010, 209161] |
220 |
C220 |
6) |
[104, 270, 16561] |
[1] |
1 |
[104, 270, 16561] |
220 |
C2 x C110 |
7) |
[3693, 97, 1429] |
[1] |
1 |
[3693, 97, 1429] |
110 |
C110 |
8) |
[213, 145, 4777] |
[1] |
1 |
[213, 145, 4777] |
110 |
C110 |
9) |
[57, 886, 163417] |
[1] |
1 |
[57, 886, 163417] |
110 |
C110 |
10) |
[57, 910, 198817] |
[1] |
1 |
[57, 910, 198817] |
110 |
C110 |
11) |
[57, 1207, 346756] |
[1] |
1 |
[57, 1207, 346756] |
110 |
C110 |
12) |
[57, 1150, 176497] |
[1] |
1 |
[57, 1150, 176497] |
110 |
C110 |
13) |
[716, 510, 62161] |
[1] |
1 |
[716, 510, 62161] |
110 |
C110 |
14) |
[377, 1071, 157732] |
[1] |
1 |
[377, 1071, 157732] |
220 |
C220 |
15) |
[13, 193, 9049] |
[3, 3] |
1 |
[13, 193, 9049] |
55 |
C55 |
16) |
[5, 833, 166441] |
[1] |
1 |
[5, 833, 166441] |
110 |
C110 |
17) |
[5, 1877, 880501] |
[1] |
1 |
[5, 1877, 880501] |
110 |
C110 |
18) |
[92, 1110, 235897] |
[1] |
1 |
[92, 1110, 235897] |
110 |
C110 |
19) |
[141, 181, 7873] |
[1] |
1 |
[141, 181, 7873] |
110 |
C110 |
20) |
[152, 678, 54121] |
[1] |
1 |
[152, 678, 54121] |
110 |
C110 |
21) |
[152, 810, 83617] |
[1] |
1 |
[152, 810, 83617] |
110 |
C110 |
22) |
[113, 1206, 247897] |
[1] |
1 |
[113, 1206, 247897] |
110 |
C110 |
23) |
[185, 462, 50401] |
[1] |
1 |
[185, 462, 50401] |
220 |
C220 |
24) |
[89, 1839, 842788] |
[1] |
1 |
[89, 1839, 842788] |
110 |
C110 |
25) |
[533, 917, 7549] |
[1] |
1 |
[533, 917, 7549] |
220 |
C2 x C110 |
26) |
[329, 998, 59497] |
[1] |
1 |
[329, 998, 59497] |
110 |
C110 |
27) |
[329, 1695, 704356] |
[1] |
1 |
[329, 1695, 704356] |
110 |
C110 |
28) |
[37, 394, 37477] |
[1] |
1 |
[37, 394, 37477] |
110 |
C110 |
29) |
[61, 985, 54661] |
[1] |
1 |
[61, 985, 54661] |
110 |
C110 |
30) |
[881, 1191, 216964] |
[1] |
1 |
[881, 1191, 216964] |
110 |
C110 |
31) |
[17, 1782, 789529] |
[1] |
1 |
[17, 1782, 789529] |
110 |
C110 |
32) |
[17, 1523, 578008] |
[1] |
1 |
[17, 1523, 578008] |
110 |
C110 |
33) |
[3449, 215, 3796] |
[1] |
1 |
[3449, 215, 3796] |
110 |
C110 |
34) |
[2969, 435, 10936] |
[1] |
1 |
[2969, 435, 10936] |
110 |
C110 |
35) |
[133, 277, 11701] |
[1] |
1 |
[133, 277, 11701] |
110 |
C110 |
36) |
[776, 374, 7033] |
[1] |
1 |
[776, 374, 7033] |
220 |
C220 |
37) |
[188, 438, 44953] |
[1] |
1 |
[188, 438, 44953] |
110 |
C110 |
38) |
[44, 1530, 576601] |
[1] |
1 |
[44, 1530, 576601] |
110 |
C110 |
39) |
[44, 1054, 200113] |
[1] |
1 |
[44, 1054, 200113] |
110 |
C110 |
40) |
[21, 1033, 215317] |
[1] |
1 |
[21, 1033, 215317] |
110 |
C110 |
41) |
[21, 1081, 281509] |
[1] |
1 |
[21, 1081, 281509] |
110 |
C110 |
42) |
[21, 1009, 182653] |
[1] |
1 |
[21, 1009, 182653] |
110 |
C110 |
43) |
[85, 769, 28309] |
[1] |
1 |
[85, 769, 28309] |
220 |
C2 x C110 |
44) |
[56, 1590, 604921] |
[1] |
1 |
[56, 1590, 604921] |
110 |
C110 |
45) |
[41, 1198, 352897] |
[1] |
1 |
[41, 1198, 352897] |
110 |
C110 |
46) |
[41, 819, 145048] |
[1] |
1 |
[41, 819, 145048] |
110 |
C110 |
47) |
[41, 166, 6233] |
[1] |
1 |
[41, 166, 6233] |
110 |
C110 |
48) |
[41, 166, 6233] |
[2, 2] |
1 |
[41, 166, 6233] |
110 |
C110 |
49) |
[1961, 963, 231352] |
[1] |
1 |
[1961, 963, 231352] |
220 |
C220 |
50) |
[365, 922, 199381] |
[1] |
1 |
[365, 922, 199381] |
220 |
C220 |
51) |
[1577, 975, 95332] |
[1] |
1 |
[1577, 975, 95332] |
110 |
C110 |
52) |
[65, 1374, 445969] |
[1] |
1 |
[65, 1374, 445969] |
220 |
C2 x C110 |
53) |
[65, 987, 126136] |
[1] |
1 |
[65, 987, 126136] |
220 |
C220 |
54) |
[65, 1166, 255649] |
[1] |
1 |
[65, 1166, 255649] |
220 |
C2 x C110 |
55) |
[65, 338, 26221] |
[1] |
1 |
[65, 338, 26221] |
220 |
C220 |
56) |
[65, 899, 169144] |
[1] |
1 |
[65, 899, 169144] |
220 |
C220 |