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 210 Igusa CM invariants of non-normal (D4) fields: 46
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 645, 69057] |
[1] |
2 |
[317, 645, 69057] |
210 |
C210 |
2) |
[157, 638, 79153] |
[1] |
1 |
[157, 638, 79153] |
105 |
C105 |
3) |
[137, 1263, 356836] |
[1] |
1 |
[137, 1263, 356836] |
105 |
C105 |
4) |
[641, 1079, 116548] |
[1] |
1 |
[641, 1079, 116548] |
105 |
C105 |
5) |
[3517, 181, 277] |
[1] |
1 |
[3517, 181, 277] |
105 |
C105 |
6) |
[13, 837, 171161] |
[1] |
1 |
[13, 837, 171161] |
105 |
C105 |
7) |
[13, 705, 124097] |
[1] |
1 |
[13, 705, 124097] |
105 |
C105 |
8) |
[13, 837, 173969] |
[1] |
1 |
[13, 837, 173969] |
105 |
C105 |
9) |
[13, 493, 58393] |
[1] |
1 |
[13, 493, 58393] |
105 |
C105 |
10) |
[13, 870, 185897] |
[1] |
1 |
[13, 870, 185897] |
105 |
C105 |
11) |
[8, 1766, 777097] |
[1] |
1 |
[8, 1766, 777097] |
105 |
C105 |
12) |
[8, 1638, 655273] |
[1] |
1 |
[8, 1638, 655273] |
105 |
C105 |
13) |
[8, 1794, 799609] |
[1] |
1 |
[8, 1794, 799609] |
105 |
C105 |
14) |
[8, 1906, 908137] |
[1] |
1 |
[8, 1906, 908137] |
105 |
C105 |
15) |
[5, 1646, 674449] |
[1] |
1 |
[5, 1646, 674449] |
105 |
C105 |
16) |
[5, 973, 221281] |
[1] |
1 |
[5, 973, 221281] |
105 |
C105 |
17) |
[5, 1454, 510529] |
[1] |
1 |
[5, 1454, 510529] |
105 |
C105 |
18) |
[5, 817, 165961] |
[1] |
1 |
[5, 817, 165961] |
105 |
C105 |
19) |
[5, 997, 248401] |
[1] |
1 |
[5, 997, 248401] |
105 |
C105 |
20) |
[5, 1681, 694189] |
[1] |
1 |
[5, 1681, 694189] |
105 |
C105 |
21) |
[5, 857, 180361] |
[1] |
1 |
[5, 857, 180361] |
105 |
C105 |
22) |
[5, 1797, 806941] |
[1] |
1 |
[5, 1797, 806941] |
105 |
C105 |
23) |
[5, 1657, 669301] |
[1] |
1 |
[5, 1657, 669301] |
105 |
C105 |
24) |
[5, 1837, 841741] |
[1] |
1 |
[5, 1837, 841741] |
105 |
C105 |
25) |
[29, 694, 97673] |
[1] |
1 |
[29, 694, 97673] |
105 |
C105 |
26) |
[29, 1245, 377581] |
[1] |
1 |
[29, 1245, 377581] |
105 |
C105 |
27) |
[1693, 173, 3673] |
[1] |
1 |
[1693, 173, 3673] |
105 |
C105 |
28) |
[1597, 213, 1361] |
[1] |
1 |
[1597, 213, 1361] |
105 |
C105 |
29) |
[113, 258, 16189] |
[1] |
1 |
[113, 258, 16189] |
105 |
C105 |
30) |
[89, 258, 7741] |
[1] |
1 |
[89, 258, 7741] |
105 |
C105 |
31) |
[89, 1118, 197137] |
[1] |
1 |
[89, 1118, 197137] |
105 |
C105 |
32) |
[37, 937, 79549] |
[1] |
1 |
[37, 937, 79549] |
105 |
C105 |
33) |
[3329, 279, 18628] |
[1] |
1 |
[3329, 279, 18628] |
105 |
C105 |
34) |
[61, 629, 87793] |
[1] |
1 |
[61, 629, 87793] |
105 |
C105 |
35) |
[17, 1487, 535924] |
[1] |
1 |
[17, 1487, 535924] |
105 |
C105 |
36) |
[17, 1251, 389716] |
[1] |
1 |
[17, 1251, 389716] |
105 |
C105 |
37) |
[1429, 285, 2801] |
[1] |
1 |
[1429, 285, 2801] |
525 |
C5 x C105 |
38) |
[181, 153, 4721] |
[1] |
1 |
[181, 153, 4721] |
105 |
C105 |
39) |
[181, 590, 60961] |
[1] |
1 |
[181, 590, 60961] |
105 |
C105 |
40) |
[389, 238, 7937] |
[1] |
1 |
[389, 238, 7937] |
105 |
C105 |
41) |
[73, 598, 47353] |
[1] |
1 |
[73, 598, 47353] |
105 |
C105 |
42) |
[41, 1374, 392593] |
[1] |
1 |
[41, 1374, 392593] |
105 |
C105 |
43) |
[41, 402, 40237] |
[1] |
1 |
[41, 402, 40237] |
105 |
C105 |
44) |
[41, 999, 230548] |
[1] |
1 |
[41, 999, 230548] |
105 |
C105 |
45) |
[397, 513, 3761] |
[1] |
1 |
[397, 513, 3761] |
105 |
C105 |
46) |
[101, 493, 36497] |
[1] |
1 |
[101, 493, 36497] |
105 |
C105 |