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 50 Igusa CM invariants of non-normal (D4) fields: 76
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[229, 117, 617] |
[1] |
1 |
[229, 117, 617] |
75 |
C75 |
2) |
[409, 103, 1732] |
[1] |
1 |
[409, 103, 1732] |
25 |
C25 |
3) |
[269, 109, 1289] |
[1] |
1 |
[269, 109, 1289] |
25 |
C25 |
4) |
[137, 607, 22756] |
[1] |
1 |
[137, 607, 22756] |
25 |
C25 |
5) |
[1964, 726, 82669] |
[1] |
2 |
[1964, 726, 82669] |
50 |
C50 |
6) |
[109, 161, 4273] |
[1] |
1 |
[109, 161, 4273] |
25 |
C25 |
7) |
[97, 223, 10468] |
[1] |
1 |
[97, 223, 10468] |
25 |
C25 |
8) |
[1709, 753, 18277] |
[1] |
1 |
[1709, 753, 18277] |
25 |
C25 |
9) |
[13, 198, 8969] |
[1] |
1 |
[13, 198, 8969] |
25 |
C25 |
10) |
[13, 189, 8537] |
[1] |
1 |
[13, 189, 8537] |
25 |
C25 |
11) |
[13, 150, 5417] |
[1] |
1 |
[13, 150, 5417] |
25 |
C25 |
12) |
[13, 222, 12113] |
[1] |
1 |
[13, 222, 12113] |
25 |
C25 |
13) |
[8, 282, 19081] |
[1] |
2 |
[8, 282, 19081] |
50 |
C50 |
14) |
[8, 1078, 151129] |
[1] |
2 |
[8, 1078, 151129] |
50 |
C50 |
15) |
[8, 1298, 342793] |
[1] |
2 |
[8, 1298, 342793] |
50 |
C50 |
16) |
[8, 1110, 268825] |
[1] |
2 |
[8, 1110, 268825] |
50 |
C5 x C10 |
17) |
[8, 482, 52249] |
[1] |
1 |
[8, 482, 52249] |
25 |
C25 |
18) |
[8, 498, 59113] |
[1] |
1 |
[8, 498, 59113] |
25 |
C5 x C5 |
19) |
[8, 594, 70537] |
[1] |
1 |
[8, 594, 70537] |
25 |
C25 |
20) |
[8, 518, 48649] |
[1] |
1 |
[8, 518, 48649] |
25 |
C5 x C5 |
21) |
[8, 410, 41737] |
[1] |
2 |
[8, 410, 41737] |
50 |
C50 |
22) |
[8, 618, 70393] |
[1] |
2 |
[8, 618, 70393] |
50 |
C50 |
23) |
[8, 658, 63241] |
[1] |
1 |
[8, 658, 63241] |
25 |
C5 x C5 |
24) |
[8, 314, 17449] |
[1] |
2 |
[8, 314, 17449] |
50 |
C50 |
25) |
[8, 222, 10273] |
[1] |
1 |
[8, 222, 10273] |
25 |
C25 |
26) |
[8, 978, 121993] |
[1] |
1 |
[8, 978, 121993] |
25 |
C25 |
27) |
[8, 154, 5281] |
[1] |
1 |
[8, 154, 5281] |
25 |
C25 |
28) |
[5, 417, 37861] |
[1] |
1 |
[5, 417, 37861] |
25 |
C5 x C5 |
29) |
[5, 481, 56929] |
[1] |
1 |
[5, 481, 56929] |
25 |
C25 |
30) |
[5, 191, 9109] |
[1] |
2 |
[5, 191, 9109] |
50 |
C50 |
31) |
[5, 453, 50101] |
[1] |
1 |
[5, 453, 50101] |
25 |
C25 |
32) |
[5, 53, 641] |
[5, 5] |
1 |
[5, 53, 641] |
5 |
C5 |
33) |
[5, 276, 17044] |
[1] |
2 |
[5, 276, 17044] |
50 |
C50 |
34) |
[5, 333, 22441] |
[1] |
1 |
[5, 333, 22441] |
25 |
C25 |
35) |
[5, 641, 99469] |
[1] |
1 |
[5, 641, 99469] |
25 |
C5 x C5 |
36) |
[5, 741, 125509] |
[1] |
1 |
[5, 741, 125509] |
25 |
C25 |
37) |
[5, 13, 41] |
[15, 15] |
2 |
[5, 13, 41] |
1 |
C1 |
38) |
[5, 1309, 414589] |
[1] |
2 |
[5, 1309, 414589] |
50 |
C50 |
39) |
[5, 374, 32089] |
[1] |
1 |
[5, 374, 32089] |
25 |
C25 |
40) |
[5, 183, 8221] |
[1] |
2 |
[5, 183, 8221] |
50 |
C50 |
41) |
[5, 206, 10429] |
[1] |
2 |
[5, 206, 10429] |
50 |
C50 |
42) |
[5, 253, 16001] |
[1] |
1 |
[5, 253, 16001] |
25 |
C25 |
43) |
[5, 317, 20161] |
[1] |
1 |
[5, 317, 20161] |
25 |
C25 |
44) |
[5, 741, 134269] |
[1] |
1 |
[5, 741, 134269] |
25 |
C25 |
45) |
[5, 378, 35221] |
[1] |
1 |
[5, 378, 35221] |
25 |
C25 |
46) |
[29, 266, 8293] |
[1] |
1 |
[29, 266, 8293] |
25 |
C25 |
47) |
[29, 629, 80053] |
[1] |
2 |
[29, 629, 80053] |
50 |
C50 |
48) |
[29, 273, 2617] |
[1] |
1 |
[29, 273, 2617] |
25 |
C25 |
49) |
[29, 189, 8053] |
[1] |
1 |
[29, 189, 8053] |
25 |
C25 |
50) |
[29, 237, 13977] |
[1] |
2 |
[29, 237, 13977] |
50 |
C50 |
51) |
[257, 91, 1492] |
[1] |
1 |
[257, 91, 1492] |
75 |
C75 |
52) |
[2281, 223, 7300] |
[1] |
1 |
[2281, 223, 7300] |
25 |
C25 |
53) |
[2953, 463, 46948] |
[1] |
1 |
[2953, 463, 46948] |
25 |
C25 |
54) |
[89, 334, 15073] |
[1] |
1 |
[89, 334, 15073] |
25 |
C25 |
55) |
[53, 205, 9857] |
[1] |
1 |
[53, 205, 9857] |
25 |
C5 x C5 |
56) |
[37, 250, 3637] |
[1] |
1 |
[37, 250, 3637] |
25 |
C25 |
57) |
[293, 105, 2097] |
[1] |
2 |
[293, 105, 2097] |
50 |
C50 |
58) |
[293, 97, 521] |
[1] |
1 |
[293, 97, 521] |
25 |
C25 |
59) |
[61, 221, 12073] |
[1] |
1 |
[61, 221, 12073] |
25 |
C25 |
60) |
[197, 90, 1237] |
[1] |
1 |
[197, 90, 1237] |
25 |
C25 |
61) |
[3413, 237, 13189] |
[1] |
1 |
[3413, 237, 13189] |
25 |
C25 |
62) |
[17, 150, 3177] |
[2, 2] |
2 |
[17, 150, 3177] |
50 |
C50 |
63) |
[17, 710, 37897] |
[1] |
1 |
[17, 710, 37897] |
25 |
C25 |
64) |
[17, 1095, 297508] |
[1] |
1 |
[17, 1095, 297508] |
25 |
C25 |
65) |
[17, 150, 3177] |
[1] |
2 |
[17, 150, 3177] |
50 |
C50 |
66) |
[17, 483, 56788] |
[1] |
1 |
[17, 483, 56788] |
25 |
C25 |
67) |
[677, 135, 325] |
[1] |
4 |
[677, 135, 325] |
100 |
C2 x C50 |
68) |
[2909, 465, 18421] |
[1] |
1 |
[2909, 465, 18421] |
25 |
C25 |
69) |
[1481, 151, 2368] |
[1] |
1 |
[1481, 151, 2368] |
25 |
C25 |
70) |
[44, 464, 21748] |
[1] |
2 |
[44, 464, 21748] |
50 |
C50 |
71) |
[44, 222, 6997] |
[1] |
2 |
[44, 222, 6997] |
50 |
C50 |
72) |
[41, 911, 186724] |
[1] |
1 |
[41, 911, 186724] |
25 |
C25 |
73) |
[2213, 825, 156325] |
[1] |
2 |
[2213, 825, 156325] |
150 |
C5 x C30 |
74) |
[353, 319, 5584] |
[1] |
1 |
[353, 319, 5584] |
25 |
C25 |
75) |
[101, 369, 3109] |
[1] |
1 |
[101, 369, 3109] |
25 |
C5 x C5 |
76) |
[172, 224, 8244] |
[1] |
2 |
[172, 224, 8244] |
50 |
C50 |