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 22 Igusa CM invariants of non-normal (D4) fields: 27
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1361, 37, 2] |
[1] |
1 |
[1361, 37, 2] |
11 |
C11 |
2) |
[109, 77, 801] |
[1] |
1 |
[109, 77, 801] |
11 |
C11 |
3) |
[97, 43, 244] |
[1] |
1 |
[97, 43, 244] |
11 |
C11 |
4) |
[8, 74, 1361] |
[1] |
1 |
[8, 74, 1361] |
11 |
C11 |
5) |
[8, 90, 2017] |
[1] |
1 |
[8, 90, 2017] |
11 |
C11 |
6) |
[5, 254, 15809] |
[1] |
1 |
[5, 254, 15809] |
11 |
C11 |
7) |
[5, 181, 8089] |
[1] |
1 |
[5, 181, 8089] |
11 |
C11 |
8) |
[5, 102, 2281] |
[1] |
1 |
[5, 102, 2281] |
11 |
C11 |
9) |
[5, 113, 3041] |
[1] |
1 |
[5, 113, 3041] |
11 |
C11 |
10) |
[5, 134, 4409] |
[1] |
1 |
[5, 134, 4409] |
11 |
C11 |
11) |
[5, 206, 8609] |
[1] |
1 |
[5, 206, 8609] |
11 |
C11 |
12) |
[5, 161, 6449] |
[1] |
1 |
[5, 161, 6449] |
11 |
C11 |
13) |
[5, 137, 4481] |
[1] |
1 |
[5, 137, 4481] |
11 |
C11 |
14) |
[5, 241, 14369] |
[1] |
1 |
[5, 241, 14369] |
11 |
C11 |
15) |
[5, 182, 7001] |
[1] |
1 |
[5, 182, 7001] |
11 |
C11 |
16) |
[5, 93, 2161] |
[1] |
1 |
[5, 93, 2161] |
11 |
C11 |
17) |
[5, 102, 2521] |
[1] |
1 |
[5, 102, 2521] |
11 |
C11 |
18) |
[5, 133, 3761] |
[1] |
1 |
[5, 133, 3761] |
11 |
C11 |
19) |
[5, 141, 4969] |
[1] |
1 |
[5, 141, 4969] |
11 |
C11 |
20) |
[5, 254, 13249] |
[1] |
1 |
[5, 254, 13249] |
11 |
C11 |
21) |
[5, 181, 7529] |
[1] |
1 |
[5, 181, 7529] |
11 |
C11 |
22) |
[2161, 71, 720] |
[1] |
1 |
[2161, 71, 720] |
11 |
C11 |
23) |
[2281, 51, 80] |
[1] |
1 |
[2281, 51, 80] |
11 |
C11 |
24) |
[89, 63, 436] |
[1] |
1 |
[89, 63, 436] |
11 |
C11 |
25) |
[61, 73, 97] |
[1] |
1 |
[61, 73, 97] |
11 |
C11 |
26) |
[73, 27, 164] |
[1] |
1 |
[73, 27, 164] |
11 |
C11 |
27) |
[41, 54, 73] |
[1] |
1 |
[41, 54, 73] |
11 |
C11 |