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 420 Igusa CM invariants of non-normal (D4) fields: 50
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1717, 165, 6377] |
[1] |
1 |
[1717, 165, 6377] |
420 |
C420 |
2) |
[157, 725, 114097] |
[1] |
1 |
[157, 725, 114097] |
210 |
C210 |
3) |
[237, 641, 71377] |
[1] |
1 |
[237, 641, 71377] |
210 |
C210 |
4) |
[301, 761, 127849] |
[1] |
1 |
[301, 761, 127849] |
210 |
C210 |
5) |
[629, 565, 34361] |
[1] |
1 |
[629, 565, 34361] |
420 |
C2 x C210 |
6) |
[88, 686, 89137] |
[1] |
1 |
[88, 686, 89137] |
210 |
C210 |
7) |
[205, 606, 88529] |
[1] |
1 |
[205, 606, 88529] |
420 |
C420 |
8) |
[253, 677, 86689] |
[1] |
1 |
[253, 677, 86689] |
210 |
C210 |
9) |
[253, 486, 42857] |
[1] |
1 |
[253, 486, 42857] |
210 |
C210 |
10) |
[844, 530, 39841] |
[1] |
1 |
[844, 530, 39841] |
210 |
C210 |
11) |
[1381, 329, 23953] |
[1] |
1 |
[1381, 329, 23953] |
210 |
C210 |
12) |
[1301, 349, 14513] |
[1] |
1 |
[1301, 349, 14513] |
210 |
C210 |
13) |
[93, 917, 207409] |
[1] |
1 |
[93, 917, 207409] |
210 |
C210 |
14) |
[1693, 177, 7409] |
[1] |
1 |
[1693, 177, 7409] |
210 |
C210 |
15) |
[757, 605, 76177] |
[1] |
1 |
[757, 605, 76177] |
210 |
C210 |
16) |
[24, 974, 237073] |
[1] |
1 |
[24, 974, 237073] |
210 |
C210 |
17) |
[24, 782, 143281] |
[1] |
1 |
[24, 782, 143281] |
210 |
C210 |
18) |
[40, 894, 195809] |
[1] |
1 |
[40, 894, 195809] |
420 |
C2 x C210 |
19) |
[973, 533, 68833] |
[1] |
1 |
[973, 533, 68833] |
210 |
C210 |
20) |
[113, 278, 17513] |
[1] |
1 |
[113, 278, 17513] |
210 |
C210 |
21) |
[565, 629, 67129] |
[1] |
1 |
[565, 629, 67129] |
420 |
C2 x C210 |
22) |
[533, 613, 55433] |
[1] |
1 |
[533, 613, 55433] |
420 |
C420 |
23) |
[341, 334, 22433] |
[1] |
1 |
[341, 334, 22433] |
210 |
C210 |
24) |
[37, 942, 221249] |
[1] |
1 |
[37, 942, 221249] |
210 |
C210 |
25) |
[321, 350, 10081] |
[1] |
1 |
[321, 350, 10081] |
630 |
C3 x C210 |
26) |
[949, 509, 45553] |
[1] |
1 |
[949, 509, 45553] |
420 |
C2 x C210 |
27) |
[293, 430, 41537] |
[1] |
1 |
[293, 430, 41537] |
210 |
C210 |
28) |
[197, 841, 168497] |
[1] |
1 |
[197, 841, 168497] |
210 |
C210 |
29) |
[173, 425, 45113] |
[1] |
1 |
[173, 425, 45113] |
210 |
C210 |
30) |
[573, 653, 82393] |
[1] |
1 |
[573, 653, 82393] |
210 |
C210 |
31) |
[133, 558, 24641] |
[1] |
1 |
[133, 558, 24641] |
210 |
C210 |
32) |
[1261, 389, 34993] |
[1] |
1 |
[1261, 389, 34993] |
420 |
C420 |
33) |
[77, 653, 98113] |
[1] |
1 |
[77, 653, 98113] |
210 |
C210 |
34) |
[77, 617, 74209] |
[1] |
1 |
[77, 617, 74209] |
210 |
C210 |
35) |
[653, 553, 29273] |
[1] |
1 |
[653, 553, 29273] |
210 |
C210 |
36) |
[44, 698, 96457] |
[1] |
1 |
[44, 698, 96457] |
210 |
C210 |
37) |
[44, 754, 127873] |
[1] |
1 |
[44, 754, 127873] |
210 |
C210 |
38) |
[1213, 413, 39913] |
[1] |
1 |
[1213, 413, 39913] |
210 |
C210 |
39) |
[389, 293, 16697] |
[1] |
1 |
[389, 293, 16697] |
210 |
C210 |
40) |
[12, 910, 205297] |
[1] |
1 |
[12, 910, 205297] |
210 |
C210 |
41) |
[12, 838, 171673] |
[1] |
1 |
[12, 838, 171673] |
210 |
C210 |
42) |
[21, 1009, 254473] |
[1] |
1 |
[21, 1009, 254473] |
210 |
C210 |
43) |
[85, 921, 209489] |
[1] |
1 |
[85, 921, 209489] |
420 |
C420 |
44) |
[85, 801, 152729] |
[1] |
1 |
[85, 801, 152729] |
420 |
C2 x C210 |
45) |
[277, 845, 172897] |
[1] |
1 |
[277, 845, 172897] |
210 |
C210 |
46) |
[73, 590, 44977] |
[1] |
1 |
[73, 590, 44977] |
210 |
C210 |
47) |
[469, 785, 153001] |
[1] |
1 |
[469, 785, 153001] |
630 |
C3 x C210 |
48) |
[469, 645, 70121] |
[1] |
1 |
[469, 645, 70121] |
630 |
C3 x C210 |
49) |
[101, 814, 164033] |
[1] |
1 |
[101, 814, 164033] |
210 |
C210 |
50) |
[69, 929, 213673] |
[1] |
1 |
[69, 929, 213673] |
210 |
C210 |