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 300 Igusa CM invariants of non-normal (D4) fields: 42
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 349, 29737] |
[1] |
1 |
[317, 349, 29737] |
150 |
C150 |
2) |
[137, 1278, 300913] |
[1] |
1 |
[137, 1278, 300913] |
150 |
C5 x C30 |
3) |
[296, 610, 90361] |
[1] |
1 |
[296, 610, 90361] |
300 |
C5 x C60 |
4) |
[129, 1399, 458308] |
[1] |
1 |
[129, 1399, 458308] |
150 |
C150 |
5) |
[104, 384, 34264] |
[1] |
1 |
[104, 384, 34264] |
300 |
C300 |
6) |
[104, 1110, 306361] |
[1] |
1 |
[104, 1110, 306361] |
300 |
C300 |
7) |
[104, 1014, 106873] |
[1] |
1 |
[104, 1014, 106873] |
300 |
C300 |
8) |
[161, 1719, 727108] |
[1] |
1 |
[161, 1719, 727108] |
150 |
C150 |
9) |
[161, 1590, 621721] |
[1] |
1 |
[161, 1590, 621721] |
150 |
C150 |
10) |
[1592, 906, 12577] |
[1] |
1 |
[1592, 906, 12577] |
150 |
C150 |
11) |
[377, 1743, 757156] |
[1] |
1 |
[377, 1743, 757156] |
300 |
C300 |
12) |
[217, 967, 233284] |
[1] |
1 |
[217, 967, 233284] |
150 |
C150 |
13) |
[13, 150, 5417] |
[4, 4] |
1 |
[13, 150, 5417] |
25 |
C25 |
14) |
[5, 1534, 570289] |
[1] |
1 |
[5, 1534, 570289] |
150 |
C150 |
15) |
[29, 1361, 383149] |
[1] |
1 |
[29, 1361, 383149] |
150 |
C5 x C30 |
16) |
[29, 757, 128581] |
[1] |
1 |
[29, 757, 128581] |
150 |
C150 |
17) |
[93, 721, 59629] |
[1] |
1 |
[93, 721, 59629] |
150 |
C150 |
18) |
[93, 1105, 129277] |
[1] |
1 |
[93, 1105, 129277] |
150 |
C5 x C30 |
19) |
[3241, 319, 18148] |
[1] |
1 |
[3241, 319, 18148] |
150 |
C150 |
20) |
[40, 982, 66841] |
[1] |
1 |
[40, 982, 66841] |
300 |
C10 x C30 |
21) |
[113, 1022, 244849] |
[1] |
1 |
[113, 1022, 244849] |
150 |
C5 x C30 |
22) |
[89, 1887, 889636] |
[1] |
1 |
[89, 1887, 889636] |
150 |
C150 |
23) |
[305, 547, 41176] |
[1] |
1 |
[305, 547, 41176] |
300 |
C300 |
24) |
[281, 1310, 388561] |
[1] |
1 |
[281, 1310, 388561] |
150 |
C150 |
25) |
[184, 454, 25033] |
[1] |
1 |
[184, 454, 25033] |
150 |
C150 |
26) |
[28, 1102, 133249] |
[1] |
1 |
[28, 1102, 133249] |
150 |
C150 |
27) |
[28, 1030, 249097] |
[1] |
1 |
[28, 1030, 249097] |
150 |
C150 |
28) |
[373, 265, 16717] |
[1] |
1 |
[373, 265, 16717] |
150 |
C150 |
29) |
[2813, 497, 4789] |
[1] |
1 |
[2813, 497, 4789] |
300 |
C10 x C30 |
30) |
[77, 921, 153829] |
[1] |
1 |
[77, 921, 153829] |
150 |
C150 |
31) |
[44, 1518, 546337] |
[1] |
1 |
[44, 1518, 546337] |
150 |
C150 |
32) |
[56, 1450, 464641] |
[1] |
1 |
[56, 1450, 464641] |
150 |
C150 |
33) |
[41, 1811, 817624] |
[1] |
1 |
[41, 1811, 817624] |
150 |
C150 |
34) |
[353, 269, 10942] |
[1] |
1 |
[353, 269, 10942] |
150 |
C150 |
35) |
[353, 1287, 329284] |
[1] |
1 |
[353, 1287, 329284] |
150 |
C150 |
36) |
[929, 1335, 378436] |
[1] |
1 |
[929, 1335, 378436] |
150 |
C150 |
37) |
[65, 453, 51286] |
[1] |
1 |
[65, 453, 51286] |
300 |
C300 |
38) |
[65, 1019, 168184] |
[1] |
1 |
[65, 1019, 168184] |
300 |
C300 |
39) |
[65, 1742, 749281] |
[1] |
1 |
[65, 1742, 749281] |
300 |
C5 x C60 |
40) |
[65, 1151, 306484] |
[1] |
1 |
[65, 1151, 306484] |
300 |
C300 |
41) |
[65, 1262, 313921] |
[1] |
1 |
[65, 1262, 313921] |
300 |
C10 x C30 |
42) |
[65, 1691, 707704] |
[1] |
1 |
[65, 1691, 707704] |
300 |
C300 |