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 98 Igusa CM invariants of non-normal (D4) fields: 39
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1117, 461, 50617] |
[1] |
1 |
[1117, 461, 50617] |
49 |
C49 |
2) |
[137, 935, 149200] |
[1] |
2 |
[137, 935, 149200] |
98 |
C7 x C14 |
3) |
[13, 701, 107377] |
[1] |
1 |
[13, 701, 107377] |
49 |
C49 |
4) |
[13, 965, 232777] |
[1] |
1 |
[13, 965, 232777] |
49 |
C49 |
5) |
[13, 582, 49529] |
[1] |
1 |
[13, 582, 49529] |
49 |
C49 |
6) |
[13, 662, 79609] |
[1] |
1 |
[13, 662, 79609] |
49 |
C49 |
7) |
[13, 621, 69497] |
[1] |
1 |
[13, 621, 69497] |
49 |
C49 |
8) |
[13, 366, 28289] |
[1] |
1 |
[13, 366, 28289] |
49 |
C49 |
9) |
[13, 782, 151009] |
[1] |
1 |
[13, 782, 151009] |
49 |
C49 |
10) |
[13, 558, 57041] |
[1] |
1 |
[13, 558, 57041] |
49 |
C49 |
11) |
[13, 653, 88321] |
[1] |
1 |
[13, 653, 88321] |
49 |
C49 |
12) |
[8, 682, 92081] |
[1] |
2 |
[8, 682, 92081] |
98 |
C98 |
13) |
[8, 1314, 340057] |
[1] |
1 |
[8, 1314, 340057] |
49 |
C49 |
14) |
[8, 1158, 284041] |
[1] |
1 |
[8, 1158, 284041] |
49 |
C49 |
15) |
[5, 957, 228681] |
[1] |
2 |
[5, 957, 228681] |
98 |
C98 |
16) |
[5, 742, 129641] |
[1] |
1 |
[5, 742, 129641] |
49 |
C49 |
17) |
[5, 766, 131009] |
[1] |
1 |
[5, 766, 131009] |
49 |
C49 |
18) |
[5, 734, 116689] |
[1] |
1 |
[5, 734, 116689] |
49 |
C49 |
19) |
[5, 814, 157649] |
[1] |
1 |
[5, 814, 157649] |
49 |
C7 x C7 |
20) |
[5, 841, 176369] |
[1] |
1 |
[5, 841, 176369] |
49 |
C49 |
21) |
[5, 841, 169409] |
[1] |
1 |
[5, 841, 169409] |
49 |
C49 |
22) |
[5, 861, 169369] |
[1] |
1 |
[5, 861, 169369] |
49 |
C49 |
23) |
[5, 709, 121889] |
[1] |
1 |
[5, 709, 121889] |
49 |
C49 |
24) |
[5, 1221, 326149] |
[1] |
1 |
[5, 1221, 326149] |
49 |
C49 |
25) |
[5, 1009, 254489] |
[1] |
1 |
[5, 1009, 254489] |
49 |
C7 x C7 |
26) |
[5, 961, 230849] |
[1] |
1 |
[5, 961, 230849] |
49 |
C49 |
27) |
[5, 781, 144289] |
[1] |
1 |
[5, 781, 144289] |
49 |
C49 |
28) |
[29, 649, 100769] |
[1] |
1 |
[29, 649, 100769] |
49 |
C49 |
29) |
[1613, 1098, 140101] |
[1] |
1 |
[1613, 1098, 140101] |
49 |
C49 |
30) |
[757, 561, 46697] |
[1] |
1 |
[757, 561, 46697] |
49 |
C49 |
31) |
[53, 526, 27617] |
[1] |
1 |
[53, 526, 27617] |
49 |
C49 |
32) |
[53, 885, 192825] |
[1] |
4 |
[53, 885, 192825] |
196 |
C14 x C14 |
33) |
[709, 557, 37681] |
[1] |
1 |
[709, 557, 37681] |
49 |
C7 x C7 |
34) |
[293, 93, 2089] |
[1] |
1 |
[293, 93, 2089] |
49 |
C49 |
35) |
[61, 261, 16649] |
[1] |
1 |
[61, 261, 16649] |
49 |
C49 |
36) |
[61, 569, 31393] |
[1] |
1 |
[61, 569, 31393] |
49 |
C49 |
37) |
[373, 825, 167825] |
[1] |
2 |
[373, 825, 167825] |
98 |
C7 x C14 |
38) |
[173, 1162, 32389] |
[1] |
2 |
[173, 1162, 32389] |
98 |
C98 |
39) |
[181, 209, 10513] |
[1] |
1 |
[181, 209, 10513] |
49 |
C49 |