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 308 Igusa CM invariants of non-normal (D4) fields: 32
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[157, 941, 221017] |
[1] |
1 |
[157, 941, 221017] |
154 |
C154 |
2) |
[301, 390, 18761] |
[1] |
1 |
[301, 390, 18761] |
154 |
C154 |
3) |
[88, 626, 97177] |
[1] |
1 |
[88, 626, 97177] |
154 |
C154 |
4) |
[349, 629, 60433] |
[1] |
1 |
[349, 629, 60433] |
154 |
C154 |
5) |
[104, 506, 40609] |
[1] |
1 |
[104, 506, 40609] |
308 |
C2 x C154 |
6) |
[205, 542, 43921] |
[1] |
1 |
[205, 542, 43921] |
308 |
C308 |
7) |
[205, 809, 152089] |
[1] |
1 |
[205, 809, 152089] |
308 |
C308 |
8) |
[309, 374, 15193] |
[1] |
1 |
[309, 374, 15193] |
154 |
C154 |
9) |
[1621, 209, 7273] |
[1] |
1 |
[1621, 209, 7273] |
154 |
C154 |
10) |
[1837, 105, 2297] |
[1] |
1 |
[1837, 105, 2297] |
154 |
C154 |
11) |
[1501, 269, 14713] |
[1] |
1 |
[1501, 269, 14713] |
154 |
C154 |
12) |
[1381, 309, 6953] |
[1] |
1 |
[1381, 309, 6953] |
154 |
C154 |
13) |
[8, 782, 138769] |
[1] |
1 |
[8, 782, 138769] |
154 |
C154 |
14) |
[268, 498, 9473] |
[1] |
1 |
[268, 498, 9473] |
154 |
C154 |
15) |
[24, 914, 207673] |
[1] |
1 |
[24, 914, 207673] |
154 |
C154 |
16) |
[1685, 181, 7769] |
[1] |
1 |
[1685, 181, 7769] |
308 |
C308 |
17) |
[1781, 133, 3977] |
[1] |
1 |
[1781, 133, 3977] |
308 |
C308 |
18) |
[417, 182, 1609] |
[1] |
1 |
[417, 182, 1609] |
154 |
C154 |
19) |
[89, 310, 22601] |
[1] |
1 |
[89, 310, 22601] |
154 |
C154 |
20) |
[53, 886, 192857] |
[1] |
1 |
[53, 886, 192857] |
154 |
C154 |
21) |
[37, 918, 208313] |
[1] |
1 |
[37, 918, 208313] |
154 |
C154 |
22) |
[37, 965, 232057] |
[1] |
1 |
[37, 965, 232057] |
154 |
C154 |
23) |
[445, 761, 135769] |
[1] |
1 |
[445, 761, 135769] |
616 |
C616 |
24) |
[61, 870, 185321] |
[1] |
1 |
[61, 870, 185321] |
154 |
C154 |
25) |
[133, 953, 226753] |
[1] |
1 |
[133, 953, 226753] |
154 |
C154 |
26) |
[12, 890, 197257] |
[1] |
1 |
[12, 890, 197257] |
154 |
C154 |
27) |
[21, 694, 108313] |
[1] |
1 |
[21, 694, 108313] |
154 |
C154 |
28) |
[85, 529, 26929] |
[1] |
1 |
[85, 529, 26929] |
308 |
C308 |
29) |
[85, 654, 72929] |
[1] |
1 |
[85, 654, 72929] |
308 |
C308 |
30) |
[69, 653, 87817] |
[1] |
1 |
[69, 653, 87817] |
154 |
C154 |
31) |
[69, 878, 191617] |
[1] |
1 |
[69, 878, 191617] |
154 |
C154 |
32) |
[69, 677, 103801] |
[1] |
1 |
[69, 677, 103801] |
154 |
C154 |