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 108 Igusa CM invariants of non-normal (D4) fields: 70
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[237, 97, 2293] |
[1] |
1 |
[237, 97, 2293] |
54 |
C54 |
2) |
[229, 97, 1837] |
[1] |
1 |
[229, 97, 1837] |
162 |
C3 x C54 |
3) |
[461, 281, 19625] |
[1] |
1 |
[461, 281, 19625] |
54 |
C54 |
4) |
[853, 85, 1593] |
[3] |
1 |
[853, 85, 1593] |
18 |
C18 |
5) |
[733, 141, 3321] |
[3] |
2 |
[733, 141, 3321] |
108 |
C6 x C18 |
6) |
[205, 109, 2509] |
[1] |
1 |
[205, 109, 2509] |
108 |
C108 |
7) |
[13, 1073, 114409] |
[1] |
1 |
[13, 1073, 114409] |
54 |
C54 |
8) |
[13, 477, 33401] |
[1] |
1 |
[13, 477, 33401] |
54 |
C54 |
9) |
[13, 350, 23137] |
[2] |
1 |
[13, 350, 23137] |
18 |
C18 |
10) |
[13, 165, 5633] |
[2, 2] |
1 |
[13, 165, 5633] |
18 |
C18 |
11) |
[8, 494, 53809] |
[1] |
1 |
[8, 494, 53809] |
54 |
C54 |
12) |
[8, 774, 141577] |
[1] |
1 |
[8, 774, 141577] |
54 |
C54 |
13) |
[8, 1050, 263457] |
[1] |
2 |
[8, 1050, 263457] |
108 |
C6 x C18 |
14) |
[8, 286, 20321] |
[1] |
1 |
[8, 286, 20321] |
54 |
C54 |
15) |
[8, 786, 104521] |
[1] |
1 |
[8, 786, 104521] |
54 |
C54 |
16) |
[8, 286, 19297] |
[1] |
1 |
[8, 286, 19297] |
54 |
C54 |
17) |
[8, 414, 34657] |
[1] |
1 |
[8, 414, 34657] |
54 |
C54 |
18) |
[8, 698, 71873] |
[1] |
1 |
[8, 698, 71873] |
54 |
C54 |
19) |
[8, 670, 73025] |
[1] |
2 |
[8, 670, 73025] |
108 |
C2 x C54 |
20) |
[8, 586, 82961] |
[1] |
1 |
[8, 586, 82961] |
54 |
C3 x C18 |
21) |
[8, 946, 223081] |
[1] |
1 |
[8, 946, 223081] |
54 |
C3 x C18 |
22) |
[8, 834, 98617] |
[1] |
1 |
[8, 834, 98617] |
54 |
C54 |
23) |
[5, 1569, 596529] |
[1] |
2 |
[5, 1569, 596529] |
108 |
C2 x C54 |
24) |
[5, 1129, 311249] |
[1] |
1 |
[5, 1129, 311249] |
54 |
C54 |
25) |
[5, 13, 41] |
[2, 38] |
1 |
[5, 13, 41] |
1 |
C1 |
26) |
[5, 1121, 295249] |
[1] |
1 |
[5, 1121, 295249] |
54 |
C54 |
27) |
[5, 374, 33689] |
[2, 2] |
1 |
[5, 374, 33689] |
18 |
C18 |
28) |
[5, 2334, 1240209] |
[1] |
2 |
[5, 2334, 1240209] |
108 |
C6 x C18 |
29) |
[5, 2529, 1342449] |
[1] |
2 |
[5, 2529, 1342449] |
108 |
C3 x C36 |
30) |
[5, 1229, 357449] |
[1] |
1 |
[5, 1229, 357449] |
54 |
C54 |
31) |
[5, 1006, 252689] |
[1] |
1 |
[5, 1006, 252689] |
54 |
C54 |
32) |
[5, 374, 31049] |
[2, 2] |
1 |
[5, 374, 31049] |
18 |
C18 |
33) |
[5, 2061, 968769] |
[1] |
2 |
[5, 2061, 968769] |
108 |
C3 x C36 |
34) |
[5, 2469, 1519929] |
[1] |
2 |
[5, 2469, 1519929] |
108 |
C2 x C54 |
35) |
[5, 1734, 648009] |
[1] |
2 |
[5, 1734, 648009] |
108 |
C2 x C54 |
36) |
[5, 1214, 322369] |
[1] |
1 |
[5, 1214, 322369] |
54 |
C54 |
37) |
[5, 861, 185329] |
[1] |
1 |
[5, 861, 185329] |
54 |
C54 |
38) |
[5, 901, 179489] |
[1] |
1 |
[5, 901, 179489] |
54 |
C3 x C18 |
39) |
[5, 1706, 675589] |
[1] |
1 |
[5, 1706, 675589] |
54 |
C54 |
40) |
[5, 1146, 272149] |
[1] |
1 |
[5, 1146, 272149] |
54 |
C54 |
41) |
[5, 2049, 925569] |
[1] |
2 |
[5, 2049, 925569] |
108 |
C3 x C36 |
42) |
[5, 326, 24569] |
[2, 2] |
1 |
[5, 326, 24569] |
18 |
C18 |
43) |
[5, 366, 32209] |
[2, 2] |
1 |
[5, 366, 32209] |
18 |
C18 |
44) |
[5, 2181, 1091889] |
[1] |
2 |
[5, 2181, 1091889] |
108 |
C108 |
45) |
[5, 1182, 342801] |
[1] |
2 |
[5, 1182, 342801] |
108 |
C2 x C54 |
46) |
[5, 1081, 252089] |
[1] |
1 |
[5, 1081, 252089] |
54 |
C54 |
47) |
[5, 886, 170329] |
[1] |
1 |
[5, 886, 170329] |
54 |
C3 x C18 |
48) |
[29, 278, 18857] |
[1] |
1 |
[29, 278, 18857] |
54 |
C54 |
49) |
[29, 125, 2681] |
[2, 2] |
1 |
[29, 125, 2681] |
18 |
C18 |
50) |
[29, 413, 41417] |
[1] |
1 |
[29, 413, 41417] |
54 |
C54 |
51) |
[24, 142, 4657] |
[1] |
1 |
[24, 142, 4657] |
54 |
C3 x C18 |
52) |
[40, 178, 7561] |
[1] |
1 |
[40, 178, 7561] |
108 |
C2 x C54 |
53) |
[509, 217, 1465] |
[1] |
1 |
[509, 217, 1465] |
54 |
C54 |
54) |
[53, 266, 15781] |
[1] |
1 |
[53, 266, 15781] |
54 |
C54 |
55) |
[33, 323, 14788] |
[1] |
1 |
[33, 323, 14788] |
54 |
C54 |
56) |
[61, 33, 257] |
[5] |
1 |
[61, 33, 257] |
9 |
C9 |
57) |
[17, 278, 5993] |
[2, 2] |
1 |
[17, 278, 5993] |
54 |
C54 |
58) |
[17, 278, 5993] |
[1] |
1 |
[17, 278, 5993] |
54 |
C54 |
59) |
[613, 181, 681] |
[1] |
1 |
[613, 181, 681] |
54 |
C54 |
60) |
[12, 710, 45337] |
[1] |
1 |
[12, 710, 45337] |
54 |
C54 |
61) |
[12, 398, 36529] |
[1] |
1 |
[12, 398, 36529] |
54 |
C54 |
62) |
[12, 890, 96457] |
[1] |
1 |
[12, 890, 96457] |
54 |
C54 |
63) |
[12, 818, 94273] |
[1] |
1 |
[12, 818, 94273] |
54 |
C3 x C18 |
64) |
[21, 121, 3529] |
[2, 2] |
1 |
[21, 121, 3529] |
18 |
C18 |
65) |
[21, 1310, 165601] |
[1] |
1 |
[21, 1310, 165601] |
54 |
C54 |
66) |
[85, 133, 2701] |
[1] |
1 |
[85, 133, 2701] |
108 |
C108 |
67) |
[41, 166, 985] |
[1] |
1 |
[41, 166, 985] |
54 |
C54 |
68) |
[41, 166, 985] |
[2, 2] |
1 |
[41, 166, 985] |
54 |
C54 |
69) |
[397, 301, 20169] |
[3] |
1 |
[397, 301, 20169] |
18 |
C18 |
70) |
[69, 278, 1657] |
[2, 2] |
1 |
[69, 278, 1657] |
18 |
C18 |