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 272 Igusa CM invariants of non-normal (D4) fields: 30
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[237, 385, 19933] |
[1] |
1 |
[237, 385, 19933] |
136 |
C136 |
2) |
[104, 578, 82585] |
[1] |
1 |
[104, 578, 82585] |
272 |
C4 x C68 |
3) |
[109, 358, 16345] |
[1] |
1 |
[109, 358, 16345] |
136 |
C2 x C68 |
4) |
[797, 245, 13213] |
[1] |
1 |
[797, 245, 13213] |
136 |
C136 |
5) |
[733, 1069, 61209] |
[1] |
1 |
[733, 1069, 61209] |
408 |
C408 |
6) |
[377, 399, 28396] |
[1] |
1 |
[377, 399, 28396] |
272 |
C4 x C68 |
7) |
[13, 550, 73753] |
[1] |
1 |
[13, 550, 73753] |
136 |
C136 |
8) |
[5, 1673, 680201] |
[1] |
1 |
[5, 1673, 680201] |
136 |
C136 |
9) |
[5, 1313, 355961] |
[1] |
1 |
[5, 1313, 355961] |
136 |
C136 |
10) |
[5, 1313, 421961] |
[1] |
1 |
[5, 1313, 421961] |
136 |
C136 |
11) |
[29, 1021, 245929] |
[1] |
1 |
[29, 1021, 245929] |
136 |
C136 |
12) |
[29, 1117, 155257] |
[1] |
1 |
[29, 1117, 155257] |
136 |
C136 |
13) |
[428, 426, 43657] |
[1] |
1 |
[428, 426, 43657] |
136 |
C136 |
14) |
[40, 418, 34681] |
[1] |
1 |
[40, 418, 34681] |
272 |
C2 x C2 x C68 |
15) |
[509, 998, 216425] |
[1] |
1 |
[509, 998, 216425] |
136 |
C136 |
16) |
[89, 251, 14660] |
[1] |
1 |
[89, 251, 14660] |
136 |
C136 |
17) |
[341, 417, 33157] |
[1] |
1 |
[341, 417, 33157] |
136 |
C136 |
18) |
[37, 1661, 653017] |
[1] |
1 |
[37, 1661, 653017] |
136 |
C136 |
19) |
[293, 441, 39757] |
[1] |
1 |
[293, 441, 39757] |
136 |
C136 |
20) |
[508, 322, 7633] |
[1] |
1 |
[508, 322, 7633] |
136 |
C2 x C68 |
21) |
[17, 662, 63593] |
[1] |
1 |
[17, 662, 63593] |
136 |
C136 |
22) |
[453, 337, 9253] |
[1] |
1 |
[453, 337, 9253] |
136 |
C136 |
23) |
[773, 249, 10669] |
[1] |
1 |
[773, 249, 10669] |
136 |
C136 |
24) |
[188, 546, 73777] |
[1] |
1 |
[188, 546, 73777] |
136 |
C2 x C68 |
25) |
[653, 317, 23653] |
[1] |
1 |
[653, 317, 23653] |
136 |
C2 x C68 |
26) |
[337, 367, 14716] |
[1] |
1 |
[337, 367, 14716] |
136 |
C2 x C68 |
27) |
[632, 330, 26593] |
[1] |
1 |
[632, 330, 26593] |
136 |
C2 x C68 |
28) |
[673, 307, 22048] |
[1] |
1 |
[673, 307, 22048] |
136 |
C2 x C68 |
29) |
[73, 1222, 231993] |
[1] |
1 |
[73, 1222, 231993] |
136 |
C136 |
30) |
[233, 447, 40108] |
[1] |
1 |
[233, 447, 40108] |
136 |
C2 x C68 |