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 304 Igusa CM invariants of non-normal (D4) fields: 30
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 449, 43981] |
[1] |
1 |
[317, 449, 43981] |
152 |
C2 x C76 |
2) |
[157, 790, 153513] |
[1] |
1 |
[157, 790, 153513] |
152 |
C152 |
3) |
[629, 333, 27565] |
[1] |
1 |
[629, 333, 27565] |
304 |
C4 x C76 |
4) |
[236, 522, 67177] |
[1] |
1 |
[236, 522, 67177] |
152 |
C2 x C76 |
5) |
[296, 482, 55417] |
[1] |
1 |
[296, 482, 55417] |
304 |
C2 x C2 x C76 |
6) |
[461, 377, 26197] |
[1] |
1 |
[461, 377, 26197] |
152 |
C2 x C76 |
7) |
[461, 1273, 279625] |
[1] |
1 |
[461, 1273, 279625] |
152 |
C152 |
8) |
[473, 399, 36844] |
[1] |
1 |
[473, 399, 36844] |
456 |
C2 x C228 |
9) |
[109, 481, 51709] |
[1] |
1 |
[109, 481, 51709] |
152 |
C2 x C76 |
10) |
[13, 1877, 874201] |
[1] |
1 |
[13, 1877, 874201] |
152 |
C152 |
11) |
[5, 1733, 728041] |
[1] |
1 |
[5, 1733, 728041] |
152 |
C152 |
12) |
[5, 1733, 750041] |
[1] |
1 |
[5, 1733, 750041] |
152 |
C152 |
13) |
[3701, 193, 985] |
[1] |
1 |
[3701, 193, 985] |
152 |
C152 |
14) |
[1109, 1489, 551785] |
[1] |
1 |
[1109, 1489, 551785] |
152 |
C152 |
15) |
[533, 381, 36157] |
[1] |
1 |
[533, 381, 36157] |
304 |
C4 x C76 |
16) |
[53, 917, 180953] |
[1] |
1 |
[53, 917, 180953] |
152 |
C152 |
17) |
[332, 450, 45313] |
[1] |
1 |
[332, 450, 45313] |
152 |
C2 x C76 |
18) |
[37, 625, 97573] |
[1] |
1 |
[37, 625, 97573] |
152 |
C2 x C76 |
19) |
[536, 362, 27937] |
[1] |
1 |
[536, 362, 27937] |
152 |
C2 x C76 |
20) |
[197, 489, 53821] |
[1] |
1 |
[197, 489, 53821] |
152 |
C152 |
21) |
[965, 165, 6565] |
[1] |
1 |
[965, 165, 6565] |
304 |
C4 x C76 |
22) |
[173, 614, 25049] |
[1] |
1 |
[173, 614, 25049] |
152 |
C152 |
23) |
[2917, 565, 44073] |
[1] |
1 |
[2917, 565, 44073] |
456 |
C456 |
24) |
[77, 549, 73021] |
[1] |
1 |
[77, 549, 73021] |
152 |
C2 x C76 |
25) |
[389, 429, 41245] |
[1] |
1 |
[389, 429, 41245] |
152 |
C2 x C76 |
26) |
[233, 182, 4553] |
[1] |
1 |
[233, 182, 4553] |
152 |
C152 |
27) |
[2309, 833, 103625] |
[1] |
1 |
[2309, 833, 103625] |
152 |
C152 |
28) |
[41, 715, 117956] |
[1] |
1 |
[41, 715, 117956] |
152 |
C152 |
29) |
[365, 405, 29965] |
[1] |
1 |
[365, 405, 29965] |
304 |
C4 x C76 |
30) |
[2213, 929, 201929] |
[1] |
1 |
[2213, 929, 201929] |
456 |
C456 |