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 364 Igusa CM invariants of non-normal (D4) fields: 36
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[344, 334, 26513] |
[1] |
1 |
[344, 334, 26513] |
182 |
C182 |
2) |
[629, 529, 13193] |
[1] |
1 |
[629, 529, 13193] |
364 |
C364 |
3) |
[236, 514, 19793] |
[1] |
1 |
[236, 514, 19793] |
182 |
C182 |
4) |
[205, 881, 189889] |
[1] |
1 |
[205, 881, 189889] |
364 |
C364 |
5) |
[13, 718, 112033] |
[1] |
1 |
[13, 718, 112033] |
182 |
C182 |
6) |
[76, 474, 36713] |
[1] |
1 |
[76, 474, 36713] |
182 |
C182 |
7) |
[76, 854, 179593] |
[1] |
1 |
[76, 854, 179593] |
182 |
C182 |
8) |
[29, 881, 192409] |
[1] |
1 |
[29, 881, 192409] |
182 |
C182 |
9) |
[24, 878, 188017] |
[1] |
1 |
[24, 878, 188017] |
182 |
C182 |
10) |
[781, 593, 72097] |
[1] |
1 |
[781, 593, 72097] |
182 |
C182 |
11) |
[40, 782, 139921] |
[1] |
1 |
[40, 782, 139921] |
364 |
C2 x C182 |
12) |
[1733, 157, 5729] |
[1] |
1 |
[1733, 157, 5729] |
182 |
C182 |
13) |
[37, 822, 159449] |
[1] |
1 |
[37, 822, 159449] |
182 |
C182 |
14) |
[949, 545, 72121] |
[1] |
1 |
[949, 545, 72121] |
364 |
C364 |
15) |
[293, 406, 22457] |
[1] |
1 |
[293, 406, 22457] |
182 |
C182 |
16) |
[61, 681, 106409] |
[1] |
1 |
[61, 681, 106409] |
182 |
C182 |
17) |
[17, 598, 76073] |
[1] |
1 |
[17, 598, 76073] |
182 |
C182 |
18) |
[17, 646, 71417] |
[1] |
1 |
[17, 646, 71417] |
182 |
C182 |
19) |
[997, 441, 6497] |
[1] |
1 |
[997, 441, 6497] |
182 |
C182 |
20) |
[573, 517, 3649] |
[1] |
1 |
[573, 517, 3649] |
182 |
C182 |
21) |
[181, 621, 68129] |
[1] |
1 |
[181, 621, 68129] |
182 |
C182 |
22) |
[1061, 481, 51209] |
[1] |
1 |
[1061, 481, 51209] |
182 |
C182 |
23) |
[1789, 129, 3713] |
[1] |
1 |
[1789, 129, 3713] |
182 |
C182 |
24) |
[1213, 377, 10969] |
[1] |
1 |
[1213, 377, 10969] |
182 |
C182 |
25) |
[613, 537, 16769] |
[1] |
1 |
[613, 537, 16769] |
182 |
C182 |
26) |
[12, 898, 197713] |
[1] |
1 |
[12, 898, 197713] |
182 |
C182 |
27) |
[21, 793, 154897] |
[1] |
1 |
[21, 793, 154897] |
182 |
C182 |
28) |
[85, 761, 135409] |
[1] |
1 |
[85, 761, 135409] |
364 |
C2 x C182 |
29) |
[85, 669, 98609] |
[1] |
1 |
[85, 669, 98609] |
364 |
C364 |
30) |
[365, 286, 14609] |
[1] |
1 |
[365, 286, 14609] |
364 |
C364 |
31) |
[101, 529, 51553] |
[1] |
1 |
[101, 529, 51553] |
182 |
C182 |
32) |
[101, 694, 94553] |
[1] |
1 |
[101, 694, 94553] |
182 |
C182 |
33) |
[172, 866, 181297] |
[1] |
1 |
[172, 866, 181297] |
182 |
C182 |
34) |
[265, 422, 6361] |
[1] |
1 |
[265, 422, 6361] |
364 |
C2 x C182 |
35) |
[69, 854, 177913] |
[1] |
1 |
[69, 854, 177913] |
182 |
C182 |
36) |
[488, 538, 13313] |
[1] |
1 |
[488, 538, 13313] |
364 |
C2 x C182 |