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 2 Igusa CM invariants of non-normal (D4) fields: 64
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[157, 25, 117] |
[1] |
1 |
[157, 25, 117] |
1 |
C1 |
2) |
[269, 17, 5] |
[1] |
1 |
[269, 17, 5] |
1 |
C1 |
3) |
[236, 32, 20] |
[1] |
2 |
[236, 32, 20] |
2 |
C2 |
4) |
[137, 35, 272] |
[1] |
1 |
[137, 35, 272] |
1 |
C1 |
5) |
[109, 17, 45] |
[1] |
1 |
[109, 17, 45] |
1 |
C1 |
6) |
[97, 94, 657] |
[1] |
1 |
[97, 94, 657] |
1 |
C1 |
7) |
[13, 29, 181] |
[1] |
1 |
[13, 29, 181] |
1 |
C1 |
8) |
[13, 41, 157] |
[1] |
1 |
[13, 41, 157] |
1 |
C1 |
9) |
[13, 9, 17] |
[1] |
1 |
[13, 9, 17] |
1 |
C1 |
10) |
[13, 18, 29] |
[1] |
1 |
[13, 18, 29] |
1 |
C1 |
11) |
[76, 18, 5] |
[1] |
2 |
[76, 18, 5] |
2 |
C2 |
12) |
[8, 50, 425] |
[1] |
2 |
[8, 50, 425] |
2 |
C2 |
13) |
[8, 66, 1017] |
[1] |
2 |
[8, 66, 1017] |
2 |
C2 |
14) |
[8, 14, 41] |
[1] |
2 |
[8, 14, 41] |
2 |
C2 |
15) |
[8, 18, 73] |
[1] |
1 |
[8, 18, 73] |
1 |
C1 |
16) |
[8, 26, 137] |
[1] |
2 |
[8, 26, 137] |
2 |
C2 |
17) |
[8, 22, 89] |
[1] |
1 |
[8, 22, 89] |
1 |
C1 |
18) |
[8, 30, 153] |
[1] |
4 |
[8, 30, 153] |
4 |
C2 x C2 |
19) |
[8, 38, 233] |
[1] |
1 |
[8, 38, 233] |
1 |
C1 |
20) |
[8, 10, 17] |
[1] |
1 |
[8, 10, 17] |
1 |
C1 |
21) |
[8, 34, 281] |
[1] |
1 |
[8, 34, 281] |
1 |
C1 |
22) |
[5, 66, 909] |
[1] |
2 |
[5, 66, 909] |
2 |
C2 |
23) |
[5, 21, 109] |
[1] |
1 |
[5, 21, 109] |
1 |
C1 |
24) |
[5, 41, 389] |
[1] |
1 |
[5, 41, 389] |
1 |
C1 |
25) |
[5, 17, 61] |
[1] |
1 |
[5, 17, 61] |
1 |
C1 |
26) |
[5, 34, 269] |
[1] |
1 |
[5, 34, 269] |
1 |
C1 |
27) |
[5, 13, 41] |
[1] |
1 |
[5, 13, 41] |
1 |
C1 |
28) |
[5, 26, 149] |
[1] |
1 |
[5, 26, 149] |
1 |
C1 |
29) |
[5, 11, 29] |
[1] |
2 |
[5, 11, 29] |
2 |
C2 |
30) |
[5, 33, 261] |
[1] |
2 |
[5, 33, 261] |
2 |
C2 |
31) |
[29, 26, 53] |
[1] |
1 |
[29, 26, 53] |
1 |
C1 |
32) |
[29, 7, 5] |
[1] |
2 |
[29, 7, 5] |
2 |
C2 |
33) |
[29, 21, 45] |
[1] |
2 |
[29, 21, 45] |
2 |
C2 |
34) |
[29, 9, 13] |
[1] |
1 |
[29, 9, 13] |
1 |
C1 |
35) |
[257, 23, 68] |
[1] |
1 |
[257, 23, 68] |
3 |
C3 |
36) |
[149, 13, 5] |
[1] |
1 |
[149, 13, 5] |
1 |
C1 |
37) |
[113, 33, 18] |
[1] |
2 |
[113, 33, 18] |
2 |
C2 |
38) |
[89, 11, 8] |
[1] |
1 |
[89, 11, 8] |
1 |
C1 |
39) |
[53, 13, 29] |
[1] |
1 |
[53, 13, 29] |
1 |
C1 |
40) |
[281, 17, 2] |
[1] |
1 |
[281, 17, 2] |
1 |
C1 |
41) |
[61, 9, 5] |
[1] |
1 |
[61, 9, 5] |
1 |
C1 |
42) |
[17, 5, 2] |
[1] |
1 |
[17, 5, 2] |
1 |
C1 |
43) |
[17, 15, 52] |
[2] |
1 |
[17, 15, 52] |
1 |
C1 |
44) |
[17, 47, 548] |
[1] |
1 |
[17, 47, 548] |
1 |
C1 |
45) |
[17, 15, 52] |
[1] |
1 |
[17, 15, 52] |
1 |
C1 |
46) |
[17, 46, 257] |
[1] |
1 |
[17, 46, 257] |
1 |
C1 |
47) |
[17, 25, 50] |
[1] |
2 |
[17, 25, 50] |
2 |
C2 |
48) |
[181, 41, 13] |
[1] |
1 |
[181, 41, 13] |
1 |
C1 |
49) |
[44, 14, 5] |
[1] |
2 |
[44, 14, 5] |
2 |
C2 |
50) |
[44, 8, 5] |
[1] |
2 |
[44, 8, 5] |
2 |
C2 |
51) |
[44, 42, 45] |
[1] |
4 |
[44, 42, 45] |
4 |
C2 x C2 |
52) |
[389, 37, 245] |
[1] |
1 |
[389, 37, 245] |
1 |
C1 |
53) |
[12, 50, 325] |
[1] |
4 |
[12, 50, 325] |
4 |
C2 x C2 |
54) |
[12, 10, 13] |
[1] |
2 |
[12, 10, 13] |
2 |
C2 |
55) |
[12, 26, 157] |
[1] |
2 |
[12, 26, 157] |
2 |
C2 |
56) |
[12, 8, 13] |
[1] |
2 |
[12, 8, 13] |
2 |
C2 |
57) |
[12, 26, 61] |
[1] |
2 |
[12, 26, 61] |
2 |
C2 |
58) |
[12, 14, 37] |
[1] |
2 |
[12, 14, 37] |
2 |
C2 |
59) |
[73, 9, 2] |
[1] |
1 |
[73, 9, 2] |
1 |
C1 |
60) |
[73, 47, 388] |
[1] |
1 |
[73, 47, 388] |
1 |
C1 |
61) |
[233, 19, 32] |
[1] |
1 |
[233, 19, 32] |
1 |
C1 |
62) |
[41, 11, 20] |
[1] |
1 |
[41, 11, 20] |
1 |
C1 |
63) |
[101, 33, 45] |
[1] |
2 |
[101, 33, 45] |
2 |
C2 |
64) |
[172, 34, 117] |
[1] |
2 |
[172, 34, 117] |
2 |
C2 |