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 504 Igusa CM invariants of non-normal (D4) fields: 53
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[165, 857, 176641] |
[1] |
1 |
[165, 857, 176641] |
504 |
C2 x C252 |
2) |
[157, 582, 44489] |
[1] |
1 |
[157, 582, 44489] |
252 |
C252 |
3) |
[349, 537, 17561] |
[1] |
1 |
[349, 537, 17561] |
252 |
C252 |
4) |
[429, 785, 148801] |
[1] |
1 |
[429, 785, 148801] |
504 |
C2 x C2 x C126 |
5) |
[357, 701, 97057] |
[1] |
1 |
[357, 701, 97057] |
504 |
C2 x C252 |
6) |
[1544, 250, 14081] |
[1] |
1 |
[1544, 250, 14081] |
504 |
C2 x C252 |
7) |
[273, 406, 1897] |
[1] |
1 |
[273, 406, 1897] |
504 |
C2 x C252 |
8) |
[109, 825, 162281] |
[1] |
1 |
[109, 825, 162281] |
252 |
C2 x C126 |
9) |
[348, 310, 11497] |
[1] |
1 |
[348, 310, 11497] |
504 |
C2 x C2 x C126 |
10) |
[1212, 386, 17857] |
[1] |
1 |
[1212, 386, 17857] |
504 |
C2 x C252 |
11) |
[380, 262, 15641] |
[1] |
1 |
[380, 262, 15641] |
504 |
C2 x C2 x C126 |
12) |
[796, 554, 48073] |
[1] |
1 |
[796, 554, 48073] |
252 |
C252 |
13) |
[1768, 138, 2993] |
[1] |
1 |
[1768, 138, 2993] |
2016 |
C2 x C6 x C168 |
14) |
[13, 853, 175321] |
[1] |
1 |
[13, 853, 175321] |
252 |
C252 |
15) |
[556, 546, 18929] |
[1] |
1 |
[556, 546, 18929] |
252 |
C2 x C126 |
16) |
[92, 598, 44873] |
[1] |
1 |
[92, 598, 44873] |
252 |
C6 x C42 |
17) |
[93, 797, 150409] |
[1] |
1 |
[93, 797, 150409] |
252 |
C252 |
18) |
[221, 397, 38905] |
[1] |
1 |
[221, 397, 38905] |
504 |
C2 x C252 |
19) |
[1464, 290, 19561] |
[1] |
1 |
[1464, 290, 19561] |
504 |
C2 x C252 |
20) |
[428, 266, 10841] |
[1] |
1 |
[428, 266, 10841] |
252 |
C252 |
21) |
[141, 589, 61033] |
[1] |
1 |
[141, 589, 61033] |
252 |
C252 |
22) |
[40, 846, 171089] |
[1] |
1 |
[40, 846, 171089] |
504 |
C2 x C2 x C126 |
23) |
[40, 842, 174001] |
[1] |
1 |
[40, 842, 174001] |
504 |
C2 x C2 x C126 |
24) |
[140, 562, 51521] |
[1] |
1 |
[140, 562, 51521] |
504 |
C2 x C6 x C42 |
25) |
[248, 562, 37049] |
[1] |
1 |
[248, 562, 37049] |
252 |
C252 |
26) |
[1068, 418, 5233] |
[1] |
1 |
[1068, 418, 5233] |
504 |
C2 x C2 x C126 |
27) |
[332, 314, 19337] |
[1] |
1 |
[332, 314, 19337] |
252 |
C3 x C84 |
28) |
[1688, 178, 6233] |
[1] |
1 |
[1688, 178, 6233] |
252 |
C2 x C126 |
29) |
[293, 613, 55193] |
[1] |
1 |
[293, 613, 55193] |
252 |
C252 |
30) |
[28, 870, 183737] |
[1] |
1 |
[28, 870, 183737] |
252 |
C2 x C126 |
31) |
[28, 882, 192689] |
[1] |
1 |
[28, 882, 192689] |
252 |
C2 x C126 |
32) |
[445, 621, 56249] |
[1] |
1 |
[445, 621, 56249] |
1008 |
C4 x C252 |
33) |
[316, 390, 36761] |
[1] |
1 |
[316, 390, 36761] |
756 |
C3 x C252 |
34) |
[597, 581, 41257] |
[1] |
1 |
[597, 581, 41257] |
252 |
C252 |
35) |
[597, 641, 77497] |
[1] |
1 |
[597, 641, 77497] |
252 |
C3 x C84 |
36) |
[492, 578, 34321] |
[1] |
1 |
[492, 578, 34321] |
504 |
C6 x C84 |
37) |
[453, 653, 73873] |
[1] |
1 |
[453, 653, 73873] |
252 |
C252 |
38) |
[645, 641, 83209] |
[1] |
1 |
[645, 641, 83209] |
504 |
C2 x C252 |
39) |
[232, 746, 120337] |
[1] |
1 |
[232, 746, 120337] |
504 |
C2 x C2 x C126 |
40) |
[77, 925, 211577] |
[1] |
1 |
[77, 925, 211577] |
252 |
C252 |
41) |
[701, 529, 19313] |
[1] |
1 |
[701, 529, 19313] |
252 |
C2 x C126 |
42) |
[21, 838, 172537] |
[1] |
1 |
[21, 838, 172537] |
252 |
C2 x C126 |
43) |
[85, 969, 234209] |
[1] |
1 |
[85, 969, 234209] |
504 |
C2 x C252 |
44) |
[277, 573, 38801] |
[1] |
1 |
[277, 573, 38801] |
252 |
C2 x C126 |
45) |
[56, 898, 198857] |
[1] |
1 |
[56, 898, 198857] |
252 |
C2 x C126 |
46) |
[41, 598, 57257] |
[1] |
1 |
[41, 598, 57257] |
252 |
C252 |
47) |
[41, 398, 36977] |
[1] |
1 |
[41, 398, 36977] |
252 |
C252 |
48) |
[172, 662, 103369] |
[1] |
1 |
[172, 662, 103369] |
252 |
C2 x C126 |
49) |
[557, 229, 11857] |
[1] |
1 |
[557, 229, 11857] |
252 |
C252 |
50) |
[717, 581, 54097] |
[1] |
1 |
[717, 581, 54097] |
252 |
C6 x C42 |
51) |
[69, 814, 155713] |
[1] |
1 |
[69, 814, 155713] |
252 |
C252 |
52) |
[989, 469, 25073] |
[1] |
1 |
[989, 469, 25073] |
252 |
C252 |
53) |
[65, 374, 33929] |
[1] |
1 |
[65, 374, 33929] |
504 |
C2 x C252 |