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 198 Igusa CM invariants of non-normal (D4) fields: 19
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1237, 1590, 552857] |
[1] |
1 |
[1237, 1590, 552857] |
99 |
C99 |
2) |
[13, 1478, 499321] |
[1] |
1 |
[13, 1478, 499321] |
99 |
C99 |
3) |
[13, 1089, 167777] |
[1] |
1 |
[13, 1089, 167777] |
99 |
C99 |
4) |
[13, 969, 214457] |
[1] |
1 |
[13, 969, 214457] |
99 |
C99 |
5) |
[5, 1969, 917729] |
[1] |
1 |
[5, 1969, 917729] |
99 |
C99 |
6) |
[5, 1669, 637529] |
[1] |
1 |
[5, 1669, 637529] |
99 |
C99 |
7) |
[5, 1521, 509329] |
[1] |
1 |
[5, 1521, 509329] |
99 |
C99 |
8) |
[5, 1222, 371321] |
[1] |
1 |
[5, 1222, 371321] |
99 |
C99 |
9) |
[5, 1909, 733409] |
[1] |
1 |
[5, 1909, 733409] |
99 |
C99 |
10) |
[5, 1681, 676409] |
[1] |
1 |
[5, 1681, 676409] |
99 |
C99 |
11) |
[5, 1509, 568609] |
[1] |
1 |
[5, 1509, 568609] |
99 |
C99 |
12) |
[5, 1734, 742009] |
[1] |
1 |
[5, 1734, 742009] |
99 |
C99 |
13) |
[5, 1077, 247201] |
[1] |
1 |
[5, 1077, 247201] |
99 |
C99 |
14) |
[5, 2389, 1201049] |
[1] |
1 |
[5, 2389, 1201049] |
99 |
C99 |
15) |
[5, 837, 156841] |
[1] |
1 |
[5, 837, 156841] |
99 |
C99 |
16) |
[5, 3174, 2483289] |
[1] |
2 |
[5, 3174, 2483289] |
198 |
C198 |
17) |
[113, 203, 6884] |
[1] |
1 |
[113, 203, 6884] |
99 |
C99 |
18) |
[17, 507, 63748] |
[1] |
1 |
[17, 507, 63748] |
99 |
C99 |
19) |
[3989, 193, 337] |
[1] |
1 |
[3989, 193, 337] |
99 |
C99 |