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 476 Igusa CM invariants of non-normal (D4) fields: 29
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[237, 761, 127657] |
[1] |
1 |
[237, 761, 127657] |
238 |
C238 |
2) |
[301, 414, 38033] |
[1] |
1 |
[301, 414, 38033] |
238 |
C238 |
3) |
[269, 805, 150641] |
[1] |
1 |
[269, 805, 150641] |
238 |
C238 |
4) |
[88, 750, 123377] |
[1] |
1 |
[88, 750, 123377] |
238 |
C238 |
5) |
[349, 845, 177721] |
[1] |
1 |
[349, 845, 177721] |
238 |
C238 |
6) |
[213, 526, 38497] |
[1] |
1 |
[213, 526, 38497] |
238 |
C238 |
7) |
[213, 737, 116569] |
[1] |
1 |
[213, 737, 116569] |
238 |
C238 |
8) |
[109, 789, 145793] |
[1] |
1 |
[109, 789, 145793] |
238 |
C238 |
9) |
[24, 754, 124633] |
[1] |
1 |
[24, 754, 124633] |
238 |
C238 |
10) |
[24, 850, 178681] |
[1] |
1 |
[24, 850, 178681] |
238 |
C238 |
11) |
[141, 670, 91921] |
[1] |
1 |
[141, 670, 91921] |
238 |
C238 |
12) |
[152, 706, 106217] |
[1] |
1 |
[152, 706, 106217] |
238 |
C238 |
13) |
[40, 522, 67121] |
[1] |
1 |
[40, 522, 67121] |
476 |
C2 x C238 |
14) |
[37, 825, 166817] |
[1] |
1 |
[37, 825, 166817] |
238 |
C238 |
15) |
[197, 598, 76793] |
[1] |
1 |
[197, 598, 76793] |
238 |
C238 |
16) |
[573, 557, 25849] |
[1] |
1 |
[573, 557, 25849] |
238 |
C238 |
17) |
[232, 542, 65089] |
[1] |
1 |
[232, 542, 65089] |
476 |
C2 x C238 |
18) |
[133, 537, 44129] |
[1] |
1 |
[133, 537, 44129] |
238 |
C238 |
19) |
[1261, 381, 28409] |
[1] |
1 |
[1261, 381, 28409] |
476 |
C2 x C238 |
20) |
[77, 593, 58633] |
[1] |
1 |
[77, 593, 58633] |
238 |
C238 |
21) |
[337, 318, 3713] |
[1] |
1 |
[337, 318, 3713] |
238 |
C238 |
22) |
[12, 802, 150001] |
[1] |
1 |
[12, 802, 150001] |
238 |
C238 |
23) |
[85, 717, 117281] |
[1] |
1 |
[85, 717, 117281] |
476 |
C2 x C238 |
24) |
[85, 981, 240569] |
[1] |
1 |
[85, 981, 240569] |
476 |
C476 |
25) |
[41, 646, 87929] |
[1] |
1 |
[41, 646, 87929] |
238 |
C238 |
26) |
[365, 661, 76289] |
[1] |
1 |
[365, 661, 76289] |
476 |
C2 x C238 |
27) |
[365, 577, 34961] |
[1] |
1 |
[365, 577, 34961] |
476 |
C2 x C238 |
28) |
[424, 570, 29921] |
[1] |
1 |
[424, 570, 29921] |
476 |
C2 x C238 |
29) |
[989, 505, 51641] |
[1] |
1 |
[989, 505, 51641] |
238 |
C238 |