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 130 Igusa CM invariants of non-normal (D4) fields: 47
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1237, 730, 88693] |
[1] |
1 |
[1237, 730, 88693] |
65 |
C65 |
2) |
[137, 863, 116836] |
[1] |
1 |
[137, 863, 116836] |
65 |
C65 |
3) |
[13, 469, 36709] |
[1] |
1 |
[13, 469, 36709] |
65 |
C65 |
4) |
[13, 781, 87877] |
[1] |
1 |
[13, 781, 87877] |
65 |
C65 |
5) |
[8, 1158, 333673] |
[1] |
1 |
[8, 1158, 333673] |
65 |
C65 |
6) |
[8, 1302, 327001] |
[1] |
1 |
[8, 1302, 327001] |
65 |
C65 |
7) |
[8, 1206, 228409] |
[1] |
1 |
[8, 1206, 228409] |
65 |
C65 |
8) |
[8, 1698, 711001] |
[1] |
1 |
[8, 1698, 711001] |
65 |
C65 |
9) |
[8, 1462, 485689] |
[1] |
1 |
[8, 1462, 485689] |
65 |
C65 |
10) |
[8, 1602, 640249] |
[1] |
1 |
[8, 1602, 640249] |
65 |
C65 |
11) |
[8, 746, 128761] |
[1] |
2 |
[8, 746, 128761] |
130 |
C130 |
12) |
[8, 1702, 710089] |
[1] |
1 |
[8, 1702, 710089] |
65 |
C65 |
13) |
[8, 698, 117193] |
[1] |
2 |
[8, 698, 117193] |
130 |
C130 |
14) |
[8, 1782, 787609] |
[1] |
1 |
[8, 1782, 787609] |
65 |
C65 |
15) |
[5, 1581, 606589] |
[1] |
1 |
[5, 1581, 606589] |
65 |
C65 |
16) |
[5, 1809, 816589] |
[1] |
1 |
[5, 1809, 816589] |
65 |
C65 |
17) |
[5, 582, 71161] |
[1] |
1 |
[5, 582, 71161] |
65 |
C65 |
18) |
[5, 909, 198769] |
[1] |
1 |
[5, 909, 198769] |
65 |
C65 |
19) |
[5, 1181, 295129] |
[1] |
1 |
[5, 1181, 295129] |
65 |
C65 |
20) |
[5, 1629, 659629] |
[1] |
1 |
[5, 1629, 659629] |
65 |
C65 |
21) |
[5, 1126, 310489] |
[1] |
1 |
[5, 1126, 310489] |
65 |
C65 |
22) |
[5, 1501, 553789] |
[1] |
1 |
[5, 1501, 553789] |
65 |
C65 |
23) |
[5, 1089, 266449] |
[1] |
1 |
[5, 1089, 266449] |
65 |
C65 |
24) |
[5, 444, 49204] |
[1] |
2 |
[5, 444, 49204] |
130 |
C130 |
25) |
[401, 983, 89092] |
[1] |
1 |
[401, 983, 89092] |
325 |
C5 x C65 |
26) |
[113, 687, 50164] |
[1] |
1 |
[113, 687, 50164] |
65 |
C65 |
27) |
[113, 1863, 866308] |
[1] |
1 |
[113, 1863, 866308] |
65 |
C65 |
28) |
[53, 378, 35509] |
[1] |
1 |
[53, 378, 35509] |
65 |
C65 |
29) |
[53, 645, 103357] |
[1] |
1 |
[53, 645, 103357] |
65 |
C65 |
30) |
[281, 879, 63268] |
[1] |
1 |
[281, 879, 63268] |
65 |
C65 |
31) |
[37, 213, 10889] |
[1] |
1 |
[37, 213, 10889] |
65 |
C65 |
32) |
[293, 109, 2897] |
[1] |
1 |
[293, 109, 2897] |
65 |
C65 |
33) |
[17, 190, 7937] |
[2, 2] |
1 |
[17, 190, 7937] |
65 |
C65 |
34) |
[17, 1382, 467689] |
[1] |
1 |
[17, 1382, 467689] |
65 |
C65 |
35) |
[17, 1438, 455761] |
[1] |
1 |
[17, 1438, 455761] |
65 |
C65 |
36) |
[17, 1510, 530857] |
[1] |
1 |
[17, 1510, 530857] |
65 |
C65 |
37) |
[17, 1470, 494257] |
[1] |
1 |
[17, 1470, 494257] |
65 |
C65 |
38) |
[17, 190, 7937] |
[1] |
1 |
[17, 190, 7937] |
65 |
C65 |
39) |
[173, 845, 90925] |
[1] |
2 |
[173, 845, 90925] |
130 |
C130 |
40) |
[173, 157, 5081] |
[1] |
1 |
[173, 157, 5081] |
65 |
C65 |
41) |
[44, 606, 10453] |
[1] |
2 |
[44, 606, 10453] |
130 |
C130 |
42) |
[41, 1287, 340036] |
[1] |
1 |
[41, 1287, 340036] |
65 |
C65 |
43) |
[41, 1743, 755812] |
[1] |
1 |
[41, 1743, 755812] |
65 |
C65 |
44) |
[41, 142, 2417] |
[2, 2] |
1 |
[41, 142, 2417] |
65 |
C65 |
45) |
[41, 142, 2417] |
[1] |
1 |
[41, 142, 2417] |
65 |
C65 |
46) |
[101, 282, 19477] |
[1] |
1 |
[101, 282, 19477] |
65 |
C65 |
47) |
[101, 681, 106825] |
[1] |
1 |
[101, 681, 106825] |
65 |
C65 |