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 330 Igusa CM invariants of non-normal (D4) fields: 18
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1697, 983, 146116] |
[1] |
1 |
[1697, 983, 146116] |
165 |
C165 |
2) |
[13, 1153, 328813] |
[1] |
1 |
[13, 1153, 328813] |
165 |
C165 |
3) |
[13, 853, 65809] |
[1] |
1 |
[13, 853, 65809] |
165 |
C165 |
4) |
[5, 1662, 680881] |
[1] |
1 |
[5, 1662, 680881] |
165 |
C165 |
5) |
[29, 1317, 337741] |
[1] |
1 |
[29, 1317, 337741] |
165 |
C165 |
6) |
[3581, 153, 4957] |
[1] |
1 |
[3581, 153, 4957] |
165 |
C165 |
7) |
[509, 1005, 78301] |
[1] |
1 |
[509, 1005, 78301] |
165 |
C165 |
8) |
[281, 1094, 137353] |
[1] |
1 |
[281, 1094, 137353] |
165 |
C165 |
9) |
[61, 901, 172069] |
[1] |
1 |
[61, 901, 172069] |
165 |
C165 |
10) |
[17, 1823, 829876] |
[1] |
1 |
[17, 1823, 829876] |
165 |
C165 |
11) |
[569, 798, 150097] |
[1] |
1 |
[569, 798, 150097] |
165 |
C165 |
12) |
[1481, 1119, 250468] |
[1] |
1 |
[1481, 1119, 250468] |
165 |
C165 |
13) |
[2621, 573, 2797] |
[1] |
1 |
[2621, 573, 2797] |
165 |
C165 |
14) |
[233, 1743, 749668] |
[1] |
1 |
[233, 1743, 749668] |
165 |
C165 |
15) |
[1193, 983, 24148] |
[1] |
1 |
[1193, 983, 24148] |
165 |
C165 |
16) |
[41, 1662, 674161] |
[1] |
1 |
[41, 1662, 674161] |
165 |
C165 |
17) |
[41, 1911, 912724] |
[1] |
1 |
[41, 1911, 912724] |
165 |
C165 |
18) |
[41, 1279, 320308] |
[1] |
1 |
[41, 1279, 320308] |
165 |
C165 |