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 190 Igusa CM invariants of non-normal (D4) fields: 23
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[137, 1791, 796132] |
[1] |
1 |
[137, 1791, 796132] |
95 |
C95 |
2) |
[13, 1021, 137029] |
[1] |
1 |
[13, 1021, 137029] |
95 |
C95 |
3) |
[13, 805, 117517] |
[1] |
1 |
[13, 805, 117517] |
95 |
C95 |
4) |
[13, 841, 171877] |
[1] |
1 |
[13, 841, 171877] |
95 |
C95 |
5) |
[8, 1862, 865609] |
[1] |
1 |
[8, 1862, 865609] |
95 |
C95 |
6) |
[8, 1394, 440809] |
[1] |
1 |
[8, 1394, 440809] |
95 |
C95 |
7) |
[5, 1761, 767869] |
[1] |
1 |
[5, 1761, 767869] |
95 |
C95 |
8) |
[5, 1206, 300889] |
[1] |
1 |
[5, 1206, 300889] |
95 |
C95 |
9) |
[5, 1286, 406969] |
[1] |
1 |
[5, 1286, 406969] |
95 |
C95 |
10) |
[5, 1406, 422209] |
[1] |
1 |
[5, 1406, 422209] |
95 |
C95 |
11) |
[5, 1173, 297421] |
[1] |
1 |
[5, 1173, 297421] |
95 |
C95 |
12) |
[29, 1053, 148957] |
[1] |
1 |
[29, 1053, 148957] |
95 |
C95 |
13) |
[29, 1173, 300997] |
[1] |
1 |
[29, 1173, 300997] |
95 |
C95 |
14) |
[193, 382, 8689] |
[1] |
1 |
[193, 382, 8689] |
95 |
C95 |
15) |
[113, 519, 49684] |
[1] |
1 |
[113, 519, 49684] |
95 |
C95 |
16) |
[53, 605, 38917] |
[1] |
1 |
[53, 605, 38917] |
95 |
C95 |
17) |
[617, 951, 14932] |
[1] |
1 |
[617, 951, 14932] |
95 |
C95 |
18) |
[653, 1473, 495253] |
[1] |
1 |
[653, 1473, 495253] |
95 |
C95 |
19) |
[41, 1214, 315313] |
[1] |
1 |
[41, 1214, 315313] |
95 |
C95 |
20) |
[41, 1278, 297457] |
[1] |
1 |
[41, 1278, 297457] |
95 |
C95 |
21) |
[353, 1223, 277828] |
[1] |
1 |
[353, 1223, 277828] |
95 |
C95 |
22) |
[101, 681, 115309] |
[1] |
1 |
[101, 681, 115309] |
95 |
C95 |
23) |
[2897, 471, 19972] |
[1] |
1 |
[2897, 471, 19972] |
95 |
C95 |