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 30 Igusa CM invariants of non-normal (D4) fields: 95
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[3761, 63, 52] |
[1] |
1 |
[3761, 63, 52] |
15 |
C15 |
2) |
[157, 154, 277] |
[1] |
1 |
[157, 154, 277] |
15 |
C15 |
3) |
[137, 231, 12484] |
[1] |
1 |
[137, 231, 12484] |
15 |
C15 |
4) |
[137, 519, 20452] |
[1] |
1 |
[137, 519, 20452] |
15 |
C15 |
5) |
[109, 37, 97] |
[1] |
1 |
[109, 37, 97] |
15 |
C15 |
6) |
[1621, 121, 13] |
[1] |
1 |
[1621, 121, 13] |
15 |
C15 |
7) |
[421, 45, 401] |
[1] |
1 |
[421, 45, 401] |
15 |
C15 |
8) |
[1409, 527, 40900] |
[1] |
1 |
[1409, 527, 40900] |
15 |
C15 |
9) |
[13, 93, 2081] |
[1] |
1 |
[13, 93, 2081] |
15 |
C15 |
10) |
[13, 97, 1621] |
[1] |
1 |
[13, 97, 1621] |
15 |
C15 |
11) |
[13, 165, 6257] |
[1] |
1 |
[13, 165, 6257] |
15 |
C15 |
12) |
[13, 209, 10657] |
[1] |
1 |
[13, 209, 10657] |
15 |
C15 |
13) |
[13, 134, 2617] |
[2, 2] |
1 |
[13, 134, 2617] |
5 |
C5 |
14) |
[8, 282, 18313] |
[1] |
2 |
[8, 282, 18313] |
30 |
C30 |
15) |
[8, 390, 35977] |
[1] |
1 |
[8, 390, 35977] |
15 |
C15 |
16) |
[8, 950, 121657] |
[1] |
2 |
[8, 950, 121657] |
30 |
C30 |
17) |
[8, 310, 19417] |
[1] |
1 |
[8, 310, 19417] |
15 |
C15 |
18) |
[8, 294, 13417] |
[1] |
1 |
[8, 294, 13417] |
15 |
C15 |
19) |
[8, 570, 80425] |
[1] |
4 |
[8, 570, 80425] |
60 |
C2 x C30 |
20) |
[8, 342, 26041] |
[1] |
1 |
[8, 342, 26041] |
15 |
C15 |
21) |
[8, 226, 12697] |
[1] |
1 |
[8, 226, 12697] |
15 |
C15 |
22) |
[8, 198, 9769] |
[1] |
1 |
[8, 198, 9769] |
15 |
C15 |
23) |
[8, 482, 32089] |
[1] |
1 |
[8, 482, 32089] |
15 |
C15 |
24) |
[8, 222, 11353] |
[1] |
2 |
[8, 222, 11353] |
30 |
C30 |
25) |
[5, 57, 661] |
[5, 5] |
1 |
[5, 57, 661] |
3 |
C3 |
26) |
[5, 193, 9161] |
[1] |
1 |
[5, 193, 9161] |
15 |
C15 |
27) |
[5, 173, 6121] |
[1] |
1 |
[5, 173, 6121] |
15 |
C15 |
28) |
[5, 42, 421] |
[2, 2, 4] |
2 |
[5, 42, 421] |
3 |
C3 |
29) |
[5, 169, 7129] |
[1] |
1 |
[5, 169, 7129] |
15 |
C15 |
30) |
[5, 174, 6849] |
[2, 2] |
2 |
[5, 174, 6849] |
10 |
C10 |
31) |
[5, 94, 1889] |
[2, 2] |
1 |
[5, 94, 1889] |
5 |
C5 |
32) |
[5, 386, 32749] |
[1] |
1 |
[5, 386, 32749] |
15 |
C15 |
33) |
[5, 81, 1609] |
[2, 2] |
1 |
[5, 81, 1609] |
5 |
C5 |
34) |
[5, 202, 8581] |
[1] |
1 |
[5, 202, 8581] |
15 |
C15 |
35) |
[5, 149, 4889] |
[2, 2] |
1 |
[5, 149, 4889] |
5 |
C5 |
36) |
[5, 237, 13381] |
[1] |
1 |
[5, 237, 13381] |
15 |
C15 |
37) |
[5, 193, 9281] |
[1] |
1 |
[5, 193, 9281] |
15 |
C15 |
38) |
[5, 314, 23029] |
[1] |
1 |
[5, 314, 23029] |
15 |
C15 |
39) |
[5, 209, 10369] |
[1] |
1 |
[5, 209, 10369] |
15 |
C15 |
40) |
[5, 214, 11369] |
[1] |
1 |
[5, 214, 11369] |
15 |
C15 |
41) |
[5, 229, 13049] |
[1] |
1 |
[5, 229, 13049] |
15 |
C15 |
42) |
[5, 229, 13009] |
[1] |
1 |
[5, 229, 13009] |
15 |
C15 |
43) |
[5, 474, 56149] |
[1] |
1 |
[5, 474, 56149] |
15 |
C15 |
44) |
[5, 153, 5641] |
[1] |
1 |
[5, 153, 5641] |
15 |
C15 |
45) |
[5, 609, 91189] |
[1] |
2 |
[5, 609, 91189] |
30 |
C30 |
46) |
[5, 317, 21061] |
[1] |
1 |
[5, 317, 21061] |
15 |
C15 |
47) |
[5, 381, 35509] |
[1] |
1 |
[5, 381, 35509] |
15 |
C15 |
48) |
[5, 241, 14489] |
[1] |
1 |
[5, 241, 14489] |
15 |
C15 |
49) |
[5, 238, 14081] |
[1] |
1 |
[5, 238, 14081] |
15 |
C15 |
50) |
[5, 394, 38629] |
[1] |
1 |
[5, 394, 38629] |
15 |
C15 |
51) |
[5, 42, 421] |
[2, 2] |
1 |
[5, 42, 421] |
3 |
C3 |
52) |
[5, 354, 30829] |
[1] |
1 |
[5, 354, 30829] |
15 |
C15 |
53) |
[5, 158, 5521] |
[1] |
1 |
[5, 158, 5521] |
15 |
C15 |
54) |
[5, 42, 421] |
[2, 2, 2] |
2 |
[5, 42, 421] |
3 |
C3 |
55) |
[5, 621, 95749] |
[1] |
2 |
[5, 621, 95749] |
30 |
C30 |
56) |
[29, 93, 937] |
[1] |
1 |
[29, 93, 937] |
15 |
C15 |
57) |
[29, 685, 18061] |
[1] |
1 |
[29, 685, 18061] |
15 |
C15 |
58) |
[29, 157, 4937] |
[1] |
1 |
[29, 157, 4937] |
15 |
C15 |
59) |
[29, 177, 7477] |
[1] |
1 |
[29, 177, 7477] |
15 |
C15 |
60) |
[29, 159, 1789] |
[1] |
2 |
[29, 159, 1789] |
30 |
C30 |
61) |
[29, 39, 373] |
[1] |
2 |
[29, 39, 373] |
30 |
C30 |
62) |
[29, 141, 4093] |
[1] |
1 |
[29, 141, 4093] |
15 |
C15 |
63) |
[1613, 645, 93925] |
[1] |
2 |
[1613, 645, 93925] |
30 |
C30 |
64) |
[953, 243, 3088] |
[1] |
1 |
[953, 243, 3088] |
15 |
C15 |
65) |
[149, 81, 709] |
[1] |
1 |
[149, 81, 709] |
15 |
C15 |
66) |
[149, 170, 1861] |
[1] |
1 |
[149, 170, 1861] |
15 |
C15 |
67) |
[509, 91, 925] |
[1] |
2 |
[509, 91, 925] |
30 |
C30 |
68) |
[89, 130, 1021] |
[1] |
1 |
[89, 130, 1021] |
15 |
C15 |
69) |
[53, 585, 6997] |
[1] |
1 |
[53, 585, 6997] |
15 |
C15 |
70) |
[53, 41, 89] |
[2, 2] |
1 |
[53, 41, 89] |
5 |
C5 |
71) |
[281, 71, 628] |
[1] |
1 |
[281, 71, 628] |
15 |
C15 |
72) |
[281, 71, 628] |
[2] |
1 |
[281, 71, 628] |
15 |
C15 |
73) |
[37, 150, 3257] |
[1] |
1 |
[37, 150, 3257] |
15 |
C15 |
74) |
[293, 65, 397] |
[1] |
1 |
[293, 65, 397] |
15 |
C15 |
75) |
[61, 185, 7321] |
[1] |
1 |
[61, 185, 7321] |
15 |
C15 |
76) |
[61, 165, 4961] |
[1] |
2 |
[61, 165, 4961] |
30 |
C30 |
77) |
[17, 210, 2797] |
[1] |
1 |
[17, 210, 2797] |
15 |
C15 |
78) |
[17, 318, 18481] |
[1] |
1 |
[17, 318, 18481] |
15 |
C15 |
79) |
[17, 631, 85732] |
[1] |
1 |
[17, 631, 85732] |
15 |
C15 |
80) |
[17, 207, 10708] |
[1] |
1 |
[17, 207, 10708] |
15 |
C15 |
81) |
[17, 207, 10708] |
[2] |
1 |
[17, 207, 10708] |
15 |
C15 |
82) |
[17, 98, 1789] |
[1] |
1 |
[17, 98, 1789] |
15 |
C15 |
83) |
[17, 558, 31873] |
[1] |
1 |
[17, 558, 31873] |
15 |
C15 |
84) |
[373, 149, 981] |
[1] |
1 |
[373, 149, 981] |
15 |
C15 |
85) |
[773, 114, 157] |
[1] |
1 |
[773, 114, 157] |
15 |
C15 |
86) |
[2393, 51, 52] |
[1] |
1 |
[2393, 51, 52] |
15 |
C15 |
87) |
[3389, 245, 7381] |
[1] |
1 |
[3389, 245, 7381] |
15 |
C15 |
88) |
[569, 327, 2692] |
[1] |
1 |
[569, 327, 2692] |
15 |
C15 |
89) |
[44, 192, 9172] |
[1] |
2 |
[44, 192, 9172] |
30 |
C30 |
90) |
[44, 84, 1588] |
[1] |
2 |
[44, 84, 1588] |
30 |
C30 |
91) |
[12, 280, 7693] |
[1] |
4 |
[12, 280, 7693] |
60 |
C2 x C30 |
92) |
[12, 94, 1621] |
[1] |
2 |
[12, 94, 1621] |
30 |
C30 |
93) |
[101, 125, 1861] |
[1] |
1 |
[101, 125, 1861] |
15 |
C15 |
94) |
[101, 215, 421] |
[1] |
2 |
[101, 215, 421] |
30 |
C30 |
95) |
[2297, 311, 19012] |
[1] |
1 |
[2297, 311, 19012] |
15 |
C15 |