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 230 Igusa CM invariants of non-normal (D4) fields: 19
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[8, 1922, 923449] |
[1] |
1 |
[8, 1922, 923449] |
115 |
C115 |
2) |
[8, 1522, 547369] |
[1] |
1 |
[8, 1522, 547369] |
115 |
C115 |
3) |
[5, 1857, 860581] |
[1] |
1 |
[5, 1857, 860581] |
115 |
C115 |
4) |
[5, 1846, 851209] |
[1] |
1 |
[5, 1846, 851209] |
115 |
C115 |
5) |
[29, 966, 186889] |
[1] |
1 |
[29, 966, 186889] |
115 |
C115 |
6) |
[29, 1089, 193813] |
[1] |
1 |
[29, 1089, 193813] |
115 |
C115 |
7) |
[29, 1013, 99877] |
[1] |
1 |
[29, 1013, 99877] |
115 |
C115 |
8) |
[29, 1905, 906901] |
[1] |
1 |
[29, 1905, 906901] |
115 |
C115 |
9) |
[29, 918, 119737] |
[1] |
1 |
[29, 918, 119737] |
115 |
C115 |
10) |
[89, 1214, 355633] |
[1] |
1 |
[89, 1214, 355633] |
115 |
C115 |
11) |
[281, 1583, 595492] |
[1] |
1 |
[281, 1583, 595492] |
115 |
C115 |
12) |
[281, 655, 76276] |
[1] |
1 |
[281, 655, 76276] |
115 |
C115 |
13) |
[593, 686, 32257] |
[1] |
1 |
[593, 686, 32257] |
115 |
C115 |
14) |
[17, 1503, 554548] |
[1] |
1 |
[17, 1503, 554548] |
115 |
C115 |
15) |
[73, 622, 86209] |
[1] |
1 |
[73, 622, 86209] |
115 |
C115 |
16) |
[41, 1391, 462964] |
[1] |
1 |
[41, 1391, 462964] |
115 |
C115 |
17) |
[241, 799, 93988] |
[1] |
1 |
[241, 799, 93988] |
115 |
C115 |
18) |
[101, 1225, 254941] |
[1] |
1 |
[101, 1225, 254941] |
115 |
C115 |
19) |
[101, 193, 8681] |
[1] |
1 |
[101, 193, 8681] |
115 |
C115 |