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 260 Igusa CM invariants of non-normal (D4) fields: 46
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[137, 357, 27718] |
[1] |
1 |
[137, 357, 27718] |
130 |
C130 |
2) |
[137, 830, 152497] |
[1] |
1 |
[137, 830, 152497] |
130 |
C130 |
3) |
[129, 226, 12253] |
[1] |
1 |
[129, 226, 12253] |
130 |
C130 |
4) |
[104, 1286, 319849] |
[1] |
1 |
[104, 1286, 319849] |
260 |
C2 x C130 |
5) |
[641, 165, 6646] |
[1] |
1 |
[641, 165, 6646] |
130 |
C130 |
6) |
[57, 1687, 711364] |
[1] |
1 |
[57, 1687, 711364] |
130 |
C130 |
7) |
[377, 915, 50872] |
[1] |
1 |
[377, 915, 50872] |
260 |
C260 |
8) |
[8, 1830, 835657] |
[1] |
1 |
[8, 1830, 835657] |
130 |
C130 |
9) |
[8, 1670, 692617] |
[1] |
1 |
[8, 1670, 692617] |
130 |
C130 |
10) |
[5, 1766, 776809] |
[1] |
1 |
[5, 1766, 776809] |
130 |
C130 |
11) |
[5, 1102, 277681] |
[1] |
1 |
[5, 1102, 277681] |
130 |
C130 |
12) |
[29, 1149, 270013] |
[1] |
1 |
[29, 1149, 270013] |
130 |
C130 |
13) |
[29, 1569, 610909] |
[1] |
1 |
[29, 1569, 610909] |
130 |
C130 |
14) |
[92, 746, 86137] |
[1] |
1 |
[92, 746, 86137] |
130 |
C130 |
15) |
[1685, 881, 8269] |
[1] |
1 |
[1685, 881, 8269] |
260 |
C2 x C130 |
16) |
[221, 990, 18721] |
[1] |
1 |
[221, 990, 18721] |
260 |
C260 |
17) |
[2489, 639, 26788] |
[1] |
1 |
[2489, 639, 26788] |
130 |
C130 |
18) |
[152, 726, 129337] |
[1] |
1 |
[152, 726, 129337] |
130 |
C130 |
19) |
[149, 765, 64021] |
[1] |
1 |
[149, 765, 64021] |
130 |
C130 |
20) |
[149, 945, 154381] |
[1] |
1 |
[149, 945, 154381] |
130 |
C130 |
21) |
[509, 929, 22213] |
[1] |
1 |
[509, 929, 22213] |
130 |
C130 |
22) |
[53, 1077, 267709] |
[1] |
1 |
[53, 1077, 267709] |
130 |
C130 |
23) |
[329, 1359, 392548] |
[1] |
1 |
[329, 1359, 392548] |
130 |
C130 |
24) |
[17, 1687, 697684] |
[1] |
1 |
[17, 1687, 697684] |
130 |
C130 |
25) |
[17, 1671, 685204] |
[1] |
1 |
[17, 1671, 685204] |
130 |
C130 |
26) |
[545, 1191, 223684] |
[1] |
1 |
[545, 1191, 223684] |
260 |
C260 |
27) |
[2969, 447, 31396] |
[1] |
1 |
[2969, 447, 31396] |
130 |
C130 |
28) |
[1241, 1103, 167332] |
[1] |
1 |
[1241, 1103, 167332] |
260 |
C260 |
29) |
[668, 962, 14929] |
[1] |
1 |
[668, 962, 14929] |
130 |
C130 |
30) |
[77, 941, 182389] |
[1] |
1 |
[77, 941, 182389] |
130 |
C130 |
31) |
[77, 801, 117877] |
[1] |
1 |
[77, 801, 117877] |
130 |
C130 |
32) |
[44, 114, 3238] |
[1] |
1 |
[44, 114, 3238] |
130 |
C130 |
33) |
[2577, 631, 67972] |
[1] |
1 |
[2577, 631, 67972] |
130 |
C130 |
34) |
[12, 1666, 674689] |
[1] |
1 |
[12, 1666, 674689] |
130 |
C130 |
35) |
[12, 1846, 851737] |
[1] |
1 |
[12, 1846, 851737] |
130 |
C130 |
36) |
[12, 1138, 318961] |
[1] |
1 |
[12, 1138, 318961] |
130 |
C130 |
37) |
[21, 997, 68821] |
[1] |
1 |
[21, 997, 68821] |
130 |
C130 |
38) |
[21, 1093, 289837] |
[1] |
1 |
[21, 1093, 289837] |
130 |
C130 |
39) |
[21, 1093, 298237] |
[1] |
1 |
[21, 1093, 298237] |
130 |
C130 |
40) |
[21, 1681, 706309] |
[1] |
1 |
[21, 1681, 706309] |
130 |
C130 |
41) |
[56, 1254, 328393] |
[1] |
1 |
[56, 1254, 328393] |
130 |
C130 |
42) |
[41, 942, 97816] |
[1] |
1 |
[41, 942, 97816] |
130 |
C130 |
43) |
[201, 895, 69556] |
[1] |
1 |
[201, 895, 69556] |
130 |
C130 |
44) |
[2105, 831, 108964] |
[1] |
1 |
[2105, 831, 108964] |
260 |
C260 |
45) |
[65, 233, 6406] |
[1] |
1 |
[65, 233, 6406] |
260 |
C260 |
46) |
[65, 1526, 544729] |
[1] |
1 |
[65, 1526, 544729] |
260 |
C260 |