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 270 Igusa CM invariants of non-normal (D4) fields: 21
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1361, 999, 69508] |
[1] |
1 |
[1361, 999, 69508] |
135 |
C135 |
2) |
[13, 2510, 1258657] |
[1] |
1 |
[13, 2510, 1258657] |
135 |
C3 x C45 |
3) |
[13, 2534, 1453657] |
[1] |
1 |
[13, 2534, 1453657] |
135 |
C135 |
4) |
[13, 1377, 217409] |
[1] |
1 |
[13, 1377, 217409] |
135 |
C3 x C45 |
5) |
[13, 1982, 965233] |
[1] |
1 |
[13, 1982, 965233] |
135 |
C135 |
6) |
[13, 961, 176797] |
[1] |
1 |
[13, 961, 176797] |
135 |
C3 x C45 |
7) |
[5, 1637, 668581] |
[1] |
1 |
[5, 1637, 668581] |
135 |
C135 |
8) |
[5, 1497, 516541] |
[1] |
1 |
[5, 1497, 516541] |
135 |
C135 |
9) |
[5, 1857, 861901] |
[1] |
1 |
[5, 1857, 861901] |
135 |
C135 |
10) |
[29, 1217, 238141] |
[1] |
1 |
[29, 1217, 238141] |
135 |
C135 |
11) |
[29, 1501, 522469] |
[1] |
1 |
[29, 1501, 522469] |
135 |
C135 |
12) |
[857, 1151, 175012] |
[1] |
1 |
[857, 1151, 175012] |
135 |
C3 x C45 |
13) |
[89, 306, 23053] |
[1] |
1 |
[89, 306, 23053] |
135 |
C135 |
14) |
[53, 1017, 83341] |
[1] |
1 |
[53, 1017, 83341] |
135 |
C135 |
15) |
[37, 174, 6977] |
[2, 2] |
1 |
[37, 174, 6977] |
45 |
C45 |
16) |
[37, 625, 73597] |
[1] |
1 |
[37, 625, 73597] |
135 |
C135 |
17) |
[541, 913, 2677] |
[1] |
1 |
[541, 913, 2677] |
135 |
C135 |
18) |
[17, 1783, 788308] |
[1] |
1 |
[17, 1783, 788308] |
135 |
C135 |
19) |
[17, 1511, 523924] |
[1] |
1 |
[17, 1511, 523924] |
135 |
C135 |
20) |
[73, 1351, 369412] |
[1] |
1 |
[73, 1351, 369412] |
135 |
C135 |
21) |
[41, 1734, 741193] |
[1] |
1 |
[41, 1734, 741193] |
135 |
C135 |