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 312 Igusa CM invariants of non-normal (D4) fields: 24
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 405, 27613] |
[1] |
1 |
[317, 405, 27613] |
156 |
C156 |
2) |
[237, 309, 13857] |
[1] |
1 |
[237, 309, 13857] |
156 |
C2 x C78 |
3) |
[437, 293, 21353] |
[1] |
1 |
[437, 293, 21353] |
156 |
C156 |
4) |
[629, 193, 7897] |
[1] |
1 |
[629, 193, 7897] |
312 |
C2 x C2 x C78 |
5) |
[269, 501, 61069] |
[1] |
1 |
[269, 501, 61069] |
156 |
C156 |
6) |
[269, 337, 22945] |
[1] |
1 |
[269, 337, 22945] |
156 |
C2 x C78 |
7) |
[145, 214, 9129] |
[1] |
1 |
[145, 214, 9129] |
624 |
C2 x C312 |
8) |
[109, 433, 45537] |
[1] |
1 |
[109, 433, 45537] |
156 |
C2 x C78 |
9) |
[205, 397, 38121] |
[1] |
1 |
[205, 397, 38121] |
312 |
C2 x C156 |
10) |
[309, 333, 23937] |
[1] |
1 |
[309, 333, 23937] |
156 |
C2 x C78 |
11) |
[413, 265, 9193] |
[1] |
1 |
[413, 265, 9193] |
156 |
C2 x C78 |
12) |
[149, 353, 24857] |
[1] |
1 |
[149, 353, 24857] |
156 |
C2 x C78 |
13) |
[509, 257, 16385] |
[1] |
1 |
[509, 257, 16385] |
156 |
C2 x C78 |
14) |
[533, 245, 14873] |
[1] |
1 |
[533, 245, 14873] |
312 |
C2 x C2 x C78 |
15) |
[37, 517, 64741] |
[1] |
1 |
[37, 517, 64741] |
156 |
C156 |
16) |
[293, 501, 62677] |
[1] |
1 |
[293, 501, 62677] |
156 |
C156 |
17) |
[581, 221, 12065] |
[1] |
1 |
[581, 221, 12065] |
156 |
C2 x C78 |
18) |
[197, 373, 30793] |
[1] |
1 |
[197, 373, 30793] |
156 |
C2 x C78 |
19) |
[197, 549, 75301] |
[1] |
1 |
[197, 549, 75301] |
156 |
C156 |
20) |
[373, 313, 22161] |
[1] |
1 |
[373, 313, 22161] |
156 |
C2 x C78 |
21) |
[173, 385, 33553] |
[1] |
1 |
[173, 385, 33553] |
156 |
C2 x C78 |
22) |
[365, 329, 26969] |
[1] |
1 |
[365, 329, 26969] |
312 |
C2 x C2 x C78 |
23) |
[101, 597, 89077] |
[1] |
1 |
[101, 597, 89077] |
156 |
C156 |
24) |
[557, 357, 28381] |
[1] |
1 |
[557, 357, 28381] |
156 |
C156 |