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 480 Igusa CM invariants of non-normal (D4) fields: 21
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 353, 31073] |
[1] |
1 |
[317, 353, 31073] |
240 |
C2 x C120 |
2) |
[236, 386, 36305] |
[1] |
1 |
[236, 386, 36305] |
240 |
C4 x C60 |
3) |
[376, 322, 25545] |
[1] |
1 |
[376, 322, 25545] |
240 |
C2 x C2 x C60 |
4) |
[348, 306, 17841] |
[1] |
1 |
[348, 306, 17841] |
480 |
C2 x C4 x C60 |
5) |
[309, 353, 30457] |
[1] |
1 |
[309, 353, 30457] |
240 |
C2 x C120 |
6) |
[636, 186, 6105] |
[1] |
1 |
[636, 186, 6105] |
480 |
C2 x C4 x C60 |
7) |
[280, 370, 33945] |
[1] |
1 |
[280, 370, 33945] |
480 |
C2 x C4 x C60 |
8) |
[92, 458, 52073] |
[1] |
1 |
[92, 458, 52073] |
240 |
C2 x C120 |
9) |
[413, 301, 21721] |
[1] |
1 |
[413, 301, 21721] |
240 |
C2 x C120 |
10) |
[105, 294, 19929] |
[1] |
1 |
[105, 294, 19929] |
480 |
C2 x C4 x C60 |
11) |
[152, 386, 33449] |
[1] |
1 |
[152, 386, 33449] |
240 |
C2 x C120 |
12) |
[156, 426, 44745] |
[1] |
1 |
[156, 426, 44745] |
480 |
C2 x C4 x C60 |
13) |
[552, 234, 13137] |
[1] |
1 |
[552, 234, 13137] |
480 |
C4 x C120 |
14) |
[293, 361, 31921] |
[1] |
1 |
[293, 361, 31921] |
240 |
C240 |
15) |
[541, 241, 14385] |
[1] |
1 |
[541, 241, 14385] |
240 |
C2 x C2 x C60 |
16) |
[492, 258, 14673] |
[1] |
1 |
[492, 258, 14673] |
480 |
C2 x C4 x C60 |
17) |
[456, 266, 13585] |
[1] |
1 |
[456, 266, 13585] |
480 |
C2 x C4 x C60 |
18) |
[77, 433, 45313] |
[1] |
1 |
[77, 433, 45313] |
240 |
C2 x C120 |
19) |
[485, 265, 16465] |
[1] |
1 |
[485, 265, 16465] |
480 |
C4 x C120 |
20) |
[520, 250, 15105] |
[1] |
1 |
[520, 250, 15105] |
960 |
C4 x C4 x C60 |
21) |
[381, 321, 25665] |
[1] |
1 |
[381, 321, 25665] |
240 |
C2 x C2 x C60 |