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 264 Igusa CM invariants of non-normal (D4) fields: 20
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[269, 353, 27857] |
[1] |
1 |
[269, 353, 27857] |
132 |
C132 |
2) |
[269, 317, 16985] |
[1] |
1 |
[269, 317, 16985] |
132 |
C2 x C66 |
3) |
[269, 293, 10097] |
[1] |
1 |
[269, 293, 10097] |
132 |
C132 |
4) |
[213, 365, 28993] |
[1] |
1 |
[213, 365, 28993] |
132 |
C132 |
5) |
[5, 209, 10769] |
[11, 11] |
1 |
[5, 209, 10769] |
12 |
C2 x C6 |
6) |
[93, 461, 52921] |
[1] |
1 |
[93, 461, 52921] |
132 |
C2 x C66 |
7) |
[413, 281, 14681] |
[1] |
1 |
[413, 281, 14681] |
132 |
C2 x C66 |
8) |
[501, 257, 15385] |
[1] |
1 |
[501, 257, 15385] |
132 |
C2 x C66 |
9) |
[197, 329, 18737] |
[1] |
1 |
[197, 329, 18737] |
132 |
C132 |
10) |
[677, 173, 7313] |
[1] |
1 |
[677, 173, 7313] |
132 |
C132 |
11) |
[677, 305, 21733] |
[1] |
1 |
[677, 305, 21733] |
132 |
C132 |
12) |
[173, 449, 40669] |
[1] |
1 |
[173, 449, 40669] |
132 |
C132 |
13) |
[573, 221, 10921] |
[1] |
1 |
[573, 221, 10921] |
132 |
C132 |
14) |
[77, 361, 28249] |
[1] |
1 |
[77, 361, 28249] |
132 |
C2 x C66 |
15) |
[701, 161, 6305] |
[1] |
1 |
[701, 161, 6305] |
132 |
C2 x C66 |
16) |
[365, 269, 7049] |
[1] |
1 |
[365, 269, 7049] |
264 |
C2 x C132 |
17) |
[101, 457, 51985] |
[1] |
1 |
[101, 457, 51985] |
132 |
C2 x C66 |
18) |
[557, 209, 4097] |
[1] |
1 |
[557, 209, 4097] |
132 |
C132 |
19) |
[557, 329, 15781] |
[1] |
1 |
[557, 329, 15781] |
132 |
C132 |
20) |
[381, 261, 5505] |
[1] |
1 |
[381, 261, 5505] |
132 |
C2 x C66 |