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 416 Igusa CM invariants of non-normal (D4) fields: 48
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[661, 718, 118305] |
[1] |
1 |
[661, 718, 118305] |
208 |
C2 x C104 |
2) |
[157, 1045, 200433] |
[1] |
1 |
[157, 1045, 200433] |
208 |
C2 x C104 |
3) |
[3669, 209, 2665] |
[1] |
1 |
[3669, 209, 2665] |
208 |
C2 x C104 |
4) |
[301, 1677, 669897] |
[1] |
1 |
[301, 1677, 669897] |
208 |
C2 x C104 |
5) |
[449, 1118, 283745] |
[1] |
1 |
[449, 1118, 283745] |
208 |
C2 x C104 |
6) |
[473, 974, 116081] |
[1] |
1 |
[473, 974, 116081] |
624 |
C624 |
7) |
[213, 1005, 171513] |
[1] |
1 |
[213, 1005, 171513] |
208 |
C2 x C104 |
8) |
[3061, 493, 23265] |
[1] |
1 |
[3061, 493, 23265] |
208 |
C2 x C104 |
9) |
[205, 1126, 107049] |
[1] |
1 |
[205, 1126, 107049] |
416 |
C4 x C104 |
10) |
[1669, 1101, 209169] |
[1] |
1 |
[1669, 1101, 209169] |
208 |
C2 x C104 |
11) |
[2269, 853, 113265] |
[1] |
1 |
[2269, 853, 113265] |
208 |
C2 x C104 |
12) |
[309, 1749, 742425] |
[1] |
1 |
[309, 1749, 742425] |
208 |
C2 x C104 |
13) |
[309, 633, 66105] |
[1] |
1 |
[309, 633, 66105] |
208 |
C2 x C104 |
14) |
[1077, 1029, 5961] |
[1] |
1 |
[1077, 1029, 5961] |
208 |
C208 |
15) |
[421, 1357, 359217] |
[1] |
1 |
[421, 1357, 359217] |
208 |
C208 |
16) |
[821, 398, 26465] |
[1] |
1 |
[821, 398, 26465] |
208 |
C2 x C104 |
17) |
[13, 1630, 654033] |
[1] |
1 |
[13, 1630, 654033] |
208 |
C2 x C104 |
18) |
[8, 2026, 1026097] |
[1] |
1 |
[8, 2026, 1026097] |
208 |
C208 |
19) |
[8, 1802, 810833] |
[1] |
1 |
[8, 1802, 810833] |
208 |
C208 |
20) |
[5, 1973, 972401] |
[1] |
1 |
[5, 1973, 972401] |
208 |
C2 x C104 |
21) |
[5, 1633, 632641] |
[1] |
1 |
[5, 1633, 632641] |
208 |
C208 |
22) |
[29, 1601, 610169] |
[1] |
1 |
[29, 1601, 610169] |
208 |
C2 x C104 |
23) |
[93, 881, 188809] |
[1] |
1 |
[93, 881, 188809] |
208 |
C2 x C104 |
24) |
[757, 145, 3553] |
[1] |
1 |
[757, 145, 3553] |
208 |
C2 x C104 |
25) |
[3005, 505, 2905] |
[1] |
1 |
[3005, 505, 2905] |
416 |
C4 x C104 |
26) |
[3781, 157, 5217] |
[1] |
1 |
[3781, 157, 5217] |
208 |
C2 x C104 |
27) |
[2077, 1005, 247833] |
[1] |
1 |
[2077, 1005, 247833] |
208 |
C2 x C104 |
28) |
[1141, 1213, 216945] |
[1] |
1 |
[1141, 1213, 216945] |
208 |
C2 x C104 |
29) |
[149, 773, 59945] |
[1] |
1 |
[149, 773, 59945] |
208 |
C2 x C104 |
30) |
[53, 1049, 93721] |
[1] |
1 |
[53, 1049, 93721] |
208 |
C2 x C104 |
31) |
[1189, 121, 985] |
[1] |
1 |
[1189, 121, 985] |
416 |
C2 x C2 x C104 |
32) |
[1933, 997, 166833] |
[1] |
1 |
[1933, 997, 166833] |
208 |
C2 x C104 |
33) |
[37, 1414, 399801] |
[1] |
1 |
[37, 1414, 399801] |
208 |
C2 x C104 |
34) |
[37, 829, 149601] |
[1] |
1 |
[37, 829, 149601] |
208 |
C2 x C104 |
35) |
[37, 1441, 452289] |
[1] |
1 |
[37, 1441, 452289] |
208 |
C2 x C104 |
36) |
[1477, 141, 4601] |
[1] |
1 |
[1477, 141, 4601] |
208 |
C208 |
37) |
[61, 1173, 258201] |
[1] |
1 |
[61, 1173, 258201] |
208 |
C2 x C104 |
38) |
[61, 1229, 228145] |
[1] |
1 |
[61, 1229, 228145] |
208 |
C2 x C104 |
39) |
[373, 1861, 865737] |
[1] |
1 |
[373, 1861, 865737] |
208 |
C2 x C104 |
40) |
[2965, 565, 79065] |
[1] |
1 |
[2965, 565, 79065] |
416 |
C4 x C104 |
41) |
[997, 1465, 494433] |
[1] |
1 |
[997, 1465, 494433] |
208 |
C208 |
42) |
[869, 1249, 231625] |
[1] |
1 |
[869, 1249, 231625] |
208 |
C2 x C104 |
43) |
[1061, 1037, 13937] |
[1] |
1 |
[1061, 1037, 13937] |
208 |
C2 x C104 |
44) |
[12, 610, 92977] |
[1] |
1 |
[12, 610, 92977] |
208 |
C208 |
45) |
[21, 1997, 996577] |
[1] |
1 |
[21, 1997, 996577] |
208 |
C208 |
46) |
[397, 1429, 427041] |
[1] |
1 |
[397, 1429, 427041] |
208 |
C208 |
47) |
[1612, 1042, 110241] |
[1] |
1 |
[1612, 1042, 110241] |
416 |
C2 x C2 x C104 |
48) |
[553, 870, 109593] |
[1] |
1 |
[553, 870, 109593] |
208 |
C2 x C104 |