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 154 Igusa CM invariants of non-normal (D4) fields: 32
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[109, 521, 61729] |
[1] |
1 |
[109, 521, 61729] |
77 |
C77 |
2) |
[1669, 185, 4801] |
[1] |
1 |
[1669, 185, 4801] |
77 |
C77 |
3) |
[13, 645, 84737] |
[1] |
1 |
[13, 645, 84737] |
77 |
C77 |
4) |
[13, 678, 89753] |
[1] |
1 |
[13, 678, 89753] |
77 |
C77 |
5) |
[8, 1938, 582793] |
[1] |
1 |
[8, 1938, 582793] |
77 |
C77 |
6) |
[8, 830, 115777] |
[1] |
1 |
[8, 830, 115777] |
77 |
C77 |
7) |
[8, 2150, 598057] |
[1] |
1 |
[8, 2150, 598057] |
77 |
C77 |
8) |
[5, 817, 156521] |
[1] |
1 |
[5, 817, 156521] |
77 |
C77 |
9) |
[5, 637, 93241] |
[1] |
1 |
[5, 637, 93241] |
77 |
C77 |
10) |
[5, 2421, 1296949] |
[1] |
1 |
[5, 2421, 1296949] |
77 |
C77 |
11) |
[5, 889, 195049] |
[1] |
1 |
[5, 889, 195049] |
77 |
C77 |
12) |
[5, 817, 157841] |
[1] |
1 |
[5, 817, 157841] |
77 |
C77 |
13) |
[5, 1001, 250489] |
[1] |
1 |
[5, 1001, 250489] |
77 |
C77 |
14) |
[5, 797, 153841] |
[1] |
1 |
[5, 797, 153841] |
77 |
C77 |
15) |
[5, 737, 118681] |
[1] |
1 |
[5, 737, 118681] |
77 |
C77 |
16) |
[5, 737, 129841] |
[1] |
1 |
[5, 737, 129841] |
77 |
C77 |
17) |
[5, 1409, 479209] |
[1] |
1 |
[5, 1409, 479209] |
77 |
C77 |
18) |
[29, 745, 134921] |
[1] |
1 |
[29, 745, 134921] |
77 |
C77 |
19) |
[29, 1530, 579541] |
[1] |
1 |
[29, 1530, 579541] |
77 |
C77 |
20) |
[37, 393, 27281] |
[1] |
1 |
[37, 393, 27281] |
77 |
C77 |
21) |
[37, 277, 5113] |
[1] |
1 |
[37, 277, 5113] |
77 |
C77 |
22) |
[61, 614, 59113] |
[1] |
1 |
[61, 614, 59113] |
77 |
C77 |
23) |
[197, 502, 12569] |
[1] |
1 |
[197, 502, 12569] |
77 |
C77 |
24) |
[197, 901, 7477] |
[1] |
1 |
[197, 901, 7477] |
77 |
C77 |
25) |
[17, 307, 23524] |
[1] |
1 |
[17, 307, 23524] |
77 |
C77 |
26) |
[677, 505, 2657] |
[1] |
1 |
[677, 505, 2657] |
77 |
C77 |
27) |
[1213, 417, 43169] |
[1] |
1 |
[1213, 417, 43169] |
77 |
C77 |
28) |
[277, 741, 117257] |
[1] |
1 |
[277, 741, 117257] |
77 |
C77 |
29) |
[277, 521, 17377] |
[1] |
1 |
[277, 521, 17377] |
77 |
C77 |
30) |
[1193, 1063, 279808] |
[1] |
1 |
[1193, 1063, 279808] |
77 |
C77 |
31) |
[41, 2246, 670729] |
[1] |
1 |
[41, 2246, 670729] |
77 |
C77 |
32) |
[41, 354, 23293] |
[1] |
1 |
[41, 354, 23293] |
77 |
C77 |