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 182 Igusa CM invariants of non-normal (D4) fields: 28
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[421, 753, 129017] |
[1] |
1 |
[421, 753, 129017] |
91 |
C91 |
2) |
[13, 873, 189593] |
[1] |
1 |
[13, 873, 189593] |
91 |
C91 |
3) |
[13, 966, 232457] |
[1] |
1 |
[13, 966, 232457] |
91 |
C91 |
4) |
[13, 957, 228569] |
[1] |
2 |
[13, 957, 228569] |
182 |
C182 |
5) |
[13, 606, 90977] |
[1] |
1 |
[13, 606, 90977] |
91 |
C91 |
6) |
[13, 597, 86369] |
[1] |
1 |
[13, 597, 86369] |
91 |
C91 |
7) |
[8, 766, 117889] |
[1] |
1 |
[8, 766, 117889] |
91 |
C91 |
8) |
[8, 2550, 1224217] |
[1] |
1 |
[8, 2550, 1224217] |
91 |
C91 |
9) |
[5, 2074, 962869] |
[1] |
1 |
[5, 2074, 962869] |
91 |
C91 |
10) |
[5, 1829, 804709] |
[1] |
1 |
[5, 1829, 804709] |
91 |
C91 |
11) |
[5, 862, 179281] |
[1] |
1 |
[5, 862, 179281] |
91 |
C91 |
12) |
[5, 937, 219281] |
[1] |
1 |
[5, 937, 219281] |
91 |
C91 |
13) |
[5, 1509, 565489] |
[1] |
1 |
[5, 1509, 565489] |
91 |
C91 |
14) |
[5, 933, 199921] |
[1] |
1 |
[5, 933, 199921] |
91 |
C91 |
15) |
[29, 766, 135089] |
[1] |
1 |
[29, 766, 135089] |
91 |
C91 |
16) |
[29, 673, 84457] |
[1] |
1 |
[29, 673, 84457] |
91 |
C91 |
17) |
[29, 789, 152433] |
[1] |
2 |
[29, 789, 152433] |
182 |
C182 |
18) |
[113, 759, 96532] |
[1] |
1 |
[113, 759, 96532] |
91 |
C91 |
19) |
[89, 294, 8793] |
[1] |
2 |
[89, 294, 8793] |
182 |
C182 |
20) |
[53, 817, 162089] |
[1] |
2 |
[53, 817, 162089] |
182 |
C182 |
21) |
[37, 730, 67957] |
[1] |
1 |
[37, 730, 67957] |
91 |
C91 |
22) |
[37, 878, 187393] |
[1] |
1 |
[37, 878, 187393] |
91 |
C91 |
23) |
[61, 486, 34649] |
[1] |
1 |
[61, 486, 34649] |
91 |
C91 |
24) |
[17, 214, 9001] |
[1] |
1 |
[17, 214, 9001] |
91 |
C91 |
25) |
[173, 606, 66897] |
[1] |
2 |
[173, 606, 66897] |
182 |
C182 |
26) |
[1013, 433, 4073] |
[1] |
1 |
[1013, 433, 4073] |
91 |
C91 |
27) |
[73, 390, 8825] |
[1] |
2 |
[73, 390, 8825] |
182 |
C182 |
28) |
[101, 750, 126081] |
[1] |
2 |
[101, 750, 126081] |
182 |
C182 |