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 54 Igusa CM invariants of non-normal (D4) fields: 49
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[269, 77, 877] |
[1] |
1 |
[269, 77, 877] |
27 |
C27 |
2) |
[137, 143, 4804] |
[2] |
1 |
[137, 143, 4804] |
9 |
C9 |
3) |
[13, 205, 10477] |
[1] |
1 |
[13, 205, 10477] |
27 |
C27 |
4) |
[13, 629, 67057] |
[1] |
1 |
[13, 629, 67057] |
27 |
C27 |
5) |
[13, 422, 27673] |
[1] |
1 |
[13, 422, 27673] |
27 |
C3 x C9 |
6) |
[13, 317, 23689] |
[1] |
1 |
[13, 317, 23689] |
27 |
C27 |
7) |
[13, 225, 7193] |
[1] |
1 |
[13, 225, 7193] |
27 |
C27 |
8) |
[13, 270, 17393] |
[1] |
1 |
[13, 270, 17393] |
27 |
C27 |
9) |
[13, 1169, 168217] |
[1] |
2 |
[13, 1169, 168217] |
54 |
C54 |
10) |
[13, 569, 59617] |
[1] |
1 |
[13, 569, 59617] |
27 |
C27 |
11) |
[8, 142, 3889] |
[1] |
1 |
[8, 142, 3889] |
27 |
C27 |
12) |
[8, 234, 6961] |
[1] |
1 |
[8, 234, 6961] |
27 |
C27 |
13) |
[8, 570, 43137] |
[1] |
2 |
[8, 570, 43137] |
54 |
C54 |
14) |
[8, 250, 7937] |
[1] |
1 |
[8, 250, 7937] |
27 |
C27 |
15) |
[8, 714, 66897] |
[1] |
2 |
[8, 714, 66897] |
54 |
C54 |
16) |
[8, 190, 5153] |
[1] |
1 |
[8, 190, 5153] |
27 |
C27 |
17) |
[5, 701, 119849] |
[1] |
1 |
[5, 701, 119849] |
27 |
C3 x C9 |
18) |
[5, 469, 50929] |
[1] |
1 |
[5, 469, 50929] |
27 |
C27 |
19) |
[5, 309, 20089] |
[1] |
1 |
[5, 309, 20089] |
27 |
C27 |
20) |
[5, 417, 43321] |
[1] |
1 |
[5, 417, 43321] |
27 |
C3 x C9 |
21) |
[5, 614, 94169] |
[1] |
1 |
[5, 614, 94169] |
27 |
C27 |
22) |
[5, 529, 66449] |
[1] |
1 |
[5, 529, 66449] |
27 |
C27 |
23) |
[5, 753, 134721] |
[1] |
2 |
[5, 753, 134721] |
54 |
C54 |
24) |
[5, 481, 48809] |
[1] |
1 |
[5, 481, 48809] |
27 |
C3 x C9 |
25) |
[5, 446, 49409] |
[1] |
1 |
[5, 446, 49409] |
27 |
C27 |
26) |
[5, 894, 196929] |
[1] |
2 |
[5, 894, 196929] |
54 |
C54 |
27) |
[5, 521, 67409] |
[1] |
1 |
[5, 521, 67409] |
27 |
C27 |
28) |
[5, 277, 18401] |
[1] |
1 |
[5, 277, 18401] |
27 |
C27 |
29) |
[5, 497, 51401] |
[1] |
2 |
[5, 497, 51401] |
54 |
C54 |
30) |
[29, 201, 10093] |
[1] |
1 |
[29, 201, 10093] |
27 |
C27 |
31) |
[257, 87, 1828] |
[2] |
1 |
[257, 87, 1828] |
27 |
C3 x C9 |
32) |
[113, 199, 9872] |
[1] |
1 |
[113, 199, 9872] |
27 |
C27 |
33) |
[113, 199, 9872] |
[2, 2] |
1 |
[113, 199, 9872] |
27 |
C27 |
34) |
[53, 102, 1753] |
[1] |
1 |
[53, 102, 1753] |
27 |
C27 |
35) |
[53, 102, 1753] |
[2, 2] |
1 |
[53, 102, 1753] |
27 |
C27 |
36) |
[37, 782, 19681] |
[1] |
1 |
[37, 782, 19681] |
27 |
C27 |
37) |
[37, 157, 5413] |
[1] |
1 |
[37, 157, 5413] |
27 |
C27 |
38) |
[61, 974, 17569] |
[1] |
1 |
[61, 974, 17569] |
27 |
C27 |
39) |
[61, 145, 4021] |
[1] |
1 |
[61, 145, 4021] |
27 |
C27 |
40) |
[197, 113, 2749] |
[1] |
1 |
[197, 113, 2749] |
27 |
C3 x C9 |
41) |
[17, 70, 953] |
[1] |
1 |
[17, 70, 953] |
27 |
C27 |
42) |
[17, 174, 7297] |
[2, 2] |
1 |
[17, 174, 7297] |
9 |
C9 |
43) |
[173, 117, 2341] |
[1] |
1 |
[173, 117, 2341] |
27 |
C3 x C9 |
44) |
[1181, 313, 10025] |
[1] |
1 |
[1181, 313, 10025] |
27 |
C27 |
45) |
[233, 95, 1732] |
[2] |
1 |
[233, 95, 1732] |
9 |
C9 |
46) |
[41, 126, 3313] |
[2, 2] |
1 |
[41, 126, 3313] |
9 |
C9 |
47) |
[397, 217, 11673] |
[1] |
1 |
[397, 217, 11673] |
27 |
C27 |
48) |
[101, 165, 6781] |
[1] |
1 |
[101, 165, 6781] |
27 |
C27 |
49) |
[101, 677, 101225] |
[1] |
1 |
[101, 677, 101225] |
27 |
C3 x C9 |