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 42 Igusa CM invariants of non-normal (D4) fields: 71
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 382, 31409] |
[1] |
1 |
[317, 382, 31409] |
21 |
C21 |
2) |
[317, 57, 733] |
[1] |
1 |
[317, 57, 733] |
21 |
C21 |
3) |
[137, 135, 3700] |
[2] |
2 |
[137, 135, 3700] |
42 |
C42 |
4) |
[137, 135, 3700] |
[1] |
2 |
[137, 135, 3700] |
42 |
C42 |
5) |
[109, 518, 4297] |
[1] |
1 |
[109, 518, 4297] |
21 |
C21 |
6) |
[797, 481, 257] |
[1] |
1 |
[797, 481, 257] |
21 |
C21 |
7) |
[1709, 169, 6713] |
[1] |
1 |
[1709, 169, 6713] |
21 |
C21 |
8) |
[13, 333, 23273] |
[1] |
2 |
[13, 333, 23273] |
42 |
C42 |
9) |
[13, 118, 1609] |
[1] |
1 |
[13, 118, 1609] |
21 |
C21 |
10) |
[13, 437, 15889] |
[1] |
1 |
[13, 437, 15889] |
21 |
C21 |
11) |
[13, 118, 1609] |
[2, 2] |
1 |
[13, 118, 1609] |
21 |
C21 |
12) |
[13, 485, 30697] |
[1] |
1 |
[13, 485, 30697] |
21 |
C21 |
13) |
[13, 157, 6133] |
[1] |
1 |
[13, 157, 6133] |
21 |
C21 |
14) |
[76, 160, 5716] |
[1] |
2 |
[76, 160, 5716] |
42 |
C42 |
15) |
[8, 306, 22441] |
[1] |
1 |
[8, 306, 22441] |
21 |
C21 |
16) |
[8, 434, 45289] |
[1] |
1 |
[8, 434, 45289] |
21 |
C21 |
17) |
[8, 486, 50857] |
[1] |
1 |
[8, 486, 50857] |
21 |
C21 |
18) |
[8, 570, 79425] |
[1] |
4 |
[8, 570, 79425] |
84 |
C2 x C42 |
19) |
[5, 889, 197029] |
[1] |
2 |
[5, 889, 197029] |
42 |
C42 |
20) |
[5, 286, 17569] |
[1] |
1 |
[5, 286, 17569] |
21 |
C21 |
21) |
[5, 198, 9721] |
[1] |
1 |
[5, 198, 9721] |
21 |
C21 |
22) |
[5, 321, 24049] |
[1] |
1 |
[5, 321, 24049] |
21 |
C21 |
23) |
[5, 609, 88069] |
[1] |
1 |
[5, 609, 88069] |
21 |
C21 |
24) |
[5, 259, 14869] |
[1] |
2 |
[5, 259, 14869] |
42 |
C42 |
25) |
[5, 629, 90709] |
[1] |
1 |
[5, 629, 90709] |
21 |
C21 |
26) |
[5, 409, 40289] |
[1] |
1 |
[5, 409, 40289] |
21 |
C21 |
27) |
[5, 334, 27809] |
[1] |
1 |
[5, 334, 27809] |
21 |
C21 |
28) |
[5, 501, 54949] |
[1] |
1 |
[5, 501, 54949] |
21 |
C21 |
29) |
[5, 333, 25621] |
[1] |
1 |
[5, 333, 25621] |
21 |
C21 |
30) |
[5, 586, 77029] |
[1] |
1 |
[5, 586, 77029] |
21 |
C21 |
31) |
[5, 361, 32369] |
[1] |
1 |
[5, 361, 32369] |
21 |
C21 |
32) |
[5, 261, 16249] |
[1] |
1 |
[5, 261, 16249] |
21 |
C21 |
33) |
[5, 714, 125029] |
[1] |
1 |
[5, 714, 125029] |
21 |
C21 |
34) |
[5, 661, 108949] |
[1] |
1 |
[5, 661, 108949] |
21 |
C21 |
35) |
[5, 449, 46889] |
[1] |
1 |
[5, 449, 46889] |
21 |
C21 |
36) |
[5, 198, 9721] |
[2, 2] |
1 |
[5, 198, 9721] |
21 |
C21 |
37) |
[5, 249, 15289] |
[1] |
1 |
[5, 249, 15289] |
21 |
C21 |
38) |
[5, 801, 129589] |
[1] |
1 |
[5, 801, 129589] |
21 |
C21 |
39) |
[5, 446, 48449] |
[1] |
1 |
[5, 446, 48449] |
21 |
C21 |
40) |
[5, 269, 18089] |
[1] |
1 |
[5, 269, 18089] |
21 |
C21 |
41) |
[5, 549, 74149] |
[1] |
1 |
[5, 549, 74149] |
21 |
C21 |
42) |
[5, 666, 98389] |
[1] |
1 |
[5, 666, 98389] |
21 |
C21 |
43) |
[5, 177, 7681] |
[1] |
1 |
[5, 177, 7681] |
21 |
C21 |
44) |
[5, 294, 21529] |
[1] |
1 |
[5, 294, 21529] |
21 |
C21 |
45) |
[5, 454, 47609] |
[1] |
1 |
[5, 454, 47609] |
21 |
C21 |
46) |
[29, 430, 8641] |
[1] |
1 |
[29, 430, 8641] |
21 |
C21 |
47) |
[29, 126, 2113] |
[2, 2] |
1 |
[29, 126, 2113] |
21 |
C21 |
48) |
[29, 126, 2113] |
[1] |
1 |
[29, 126, 2113] |
21 |
C21 |
49) |
[1637, 1050, 111925] |
[1] |
2 |
[1637, 1050, 111925] |
42 |
C42 |
50) |
[149, 129, 3229] |
[1] |
1 |
[149, 129, 3229] |
21 |
C21 |
51) |
[149, 117, 1597] |
[1] |
1 |
[149, 117, 1597] |
21 |
C21 |
52) |
[1453, 237, 4961] |
[1] |
1 |
[1453, 237, 4961] |
21 |
C21 |
53) |
[113, 299, 22096] |
[1] |
1 |
[113, 299, 22096] |
21 |
C21 |
54) |
[1229, 41, 113] |
[1] |
1 |
[1229, 41, 113] |
63 |
C3 x C21 |
55) |
[53, 313, 6353] |
[1] |
1 |
[53, 313, 6353] |
21 |
C21 |
56) |
[37, 237, 5153] |
[1] |
1 |
[37, 237, 5153] |
21 |
C21 |
57) |
[37, 126, 1601] |
[1] |
1 |
[37, 126, 1601] |
21 |
C21 |
58) |
[37, 31, 157] |
[1] |
2 |
[37, 31, 157] |
42 |
C42 |
59) |
[293, 69, 1117] |
[1] |
1 |
[293, 69, 1117] |
21 |
C21 |
60) |
[293, 329, 617] |
[1] |
1 |
[293, 329, 617] |
21 |
C21 |
61) |
[197, 133, 433] |
[1] |
1 |
[197, 133, 433] |
21 |
C21 |
62) |
[197, 566, 1289] |
[1] |
1 |
[197, 566, 1289] |
21 |
C21 |
63) |
[173, 285, 4693] |
[1] |
2 |
[173, 285, 4693] |
42 |
C42 |
64) |
[1429, 305, 20041] |
[1] |
1 |
[1429, 305, 20041] |
105 |
C105 |
65) |
[12, 136, 1741] |
[1] |
2 |
[12, 136, 1741] |
42 |
C42 |
66) |
[277, 393, 30233] |
[1] |
1 |
[277, 393, 30233] |
21 |
C21 |
67) |
[73, 175, 7492] |
[1] |
1 |
[73, 175, 7492] |
21 |
C21 |
68) |
[1609, 59, 468] |
[1] |
1 |
[1609, 59, 468] |
21 |
C21 |
69) |
[353, 1011, 181312] |
[1] |
1 |
[353, 1011, 181312] |
21 |
C21 |
70) |
[101, 429, 18513] |
[1] |
4 |
[101, 429, 18513] |
84 |
C2 x C42 |
71) |
[557, 77, 229] |
[1] |
1 |
[557, 77, 229] |
21 |
C21 |