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 350 Igusa CM invariants of non-normal (D4) fields: 25
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1069, 485, 56401] |
[1] |
1 |
[1069, 485, 56401] |
175 |
C175 |
2) |
[1049, 999, 28948] |
[1] |
1 |
[1049, 999, 28948] |
175 |
C175 |
3) |
[1289, 1119, 196708] |
[1] |
1 |
[1289, 1119, 196708] |
175 |
C175 |
4) |
[1289, 1295, 416356] |
[1] |
1 |
[1289, 1295, 416356] |
175 |
C175 |
5) |
[13, 958, 137713] |
[1] |
1 |
[13, 958, 137713] |
175 |
C175 |
6) |
[13, 1273, 329053] |
[1] |
1 |
[13, 1273, 329053] |
175 |
C175 |
7) |
[5, 1822, 827041] |
[1] |
1 |
[5, 1822, 827041] |
175 |
C175 |
8) |
[29, 1789, 796933] |
[1] |
1 |
[29, 1789, 796933] |
175 |
C175 |
9) |
[29, 917, 195541] |
[1] |
1 |
[29, 917, 195541] |
175 |
C175 |
10) |
[29, 1669, 677533] |
[1] |
1 |
[29, 1669, 677533] |
175 |
C5 x C35 |
11) |
[149, 805, 151241] |
[1] |
1 |
[149, 805, 151241] |
175 |
C175 |
12) |
[149, 598, 51257] |
[1] |
1 |
[149, 598, 51257] |
175 |
C175 |
13) |
[53, 1197, 302221] |
[1] |
1 |
[53, 1197, 302221] |
175 |
C5 x C35 |
14) |
[53, 910, 206177] |
[1] |
1 |
[53, 910, 206177] |
175 |
C175 |
15) |
[37, 945, 222137] |
[1] |
1 |
[37, 945, 222137] |
175 |
C175 |
16) |
[37, 861, 182657] |
[1] |
1 |
[37, 861, 182657] |
175 |
C175 |
17) |
[61, 774, 134153] |
[1] |
1 |
[61, 774, 134153] |
175 |
C175 |
18) |
[61, 989, 244393] |
[1] |
1 |
[61, 989, 244393] |
175 |
C175 |
19) |
[173, 673, 90353] |
[1] |
1 |
[173, 673, 90353] |
175 |
C175 |
20) |
[181, 513, 27737] |
[1] |
1 |
[181, 513, 27737] |
175 |
C175 |
21) |
[701, 510, 20161] |
[1] |
1 |
[701, 510, 20161] |
175 |
C175 |
22) |
[41, 550, 43481] |
[1] |
1 |
[41, 550, 43481] |
175 |
C175 |
23) |
[241, 470, 20521] |
[1] |
1 |
[241, 470, 20521] |
175 |
C175 |
24) |
[101, 569, 80713] |
[1] |
1 |
[101, 569, 80713] |
175 |
C175 |
25) |
[101, 790, 149561] |
[1] |
1 |
[101, 790, 149561] |
175 |
C175 |