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 150 Igusa CM invariants of non-normal (D4) fields: 68
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[157, 353, 31113] |
[1] |
1 |
[157, 353, 31113] |
75 |
C75 |
2) |
[157, 177, 7793] |
[1] |
1 |
[157, 177, 7793] |
75 |
C75 |
3) |
[449, 778, 135157] |
[1] |
1 |
[449, 778, 135157] |
75 |
C75 |
4) |
[137, 210, 10477] |
[1] |
1 |
[137, 210, 10477] |
75 |
C75 |
5) |
[137, 1455, 500452] |
[1] |
1 |
[137, 1455, 500452] |
75 |
C75 |
6) |
[97, 1087, 111844] |
[1] |
1 |
[97, 1087, 111844] |
75 |
C75 |
7) |
[13, 198, 8969] |
[2, 2] |
1 |
[13, 198, 8969] |
25 |
C25 |
8) |
[13, 222, 12113] |
[2, 2] |
1 |
[13, 222, 12113] |
25 |
C25 |
9) |
[13, 150, 5417] |
[2, 2] |
1 |
[13, 150, 5417] |
25 |
C25 |
10) |
[13, 244, 13012] |
[1] |
2 |
[13, 244, 13012] |
150 |
C150 |
11) |
[977, 963, 143668] |
[1] |
1 |
[977, 963, 143668] |
75 |
C75 |
12) |
[8, 1526, 540697] |
[1] |
1 |
[8, 1526, 540697] |
75 |
C75 |
13) |
[8, 462, 53233] |
[1] |
1 |
[8, 462, 53233] |
75 |
C75 |
14) |
[8, 1446, 460777] |
[1] |
1 |
[8, 1446, 460777] |
75 |
C75 |
15) |
[8, 1330, 421417] |
[1] |
1 |
[8, 1330, 421417] |
75 |
C5 x C15 |
16) |
[8, 1302, 386809] |
[1] |
1 |
[8, 1302, 386809] |
75 |
C75 |
17) |
[8, 1590, 626617] |
[1] |
1 |
[8, 1590, 626617] |
75 |
C75 |
18) |
[8, 1570, 604057] |
[1] |
1 |
[8, 1570, 604057] |
75 |
C75 |
19) |
[8, 1910, 911737] |
[1] |
1 |
[8, 1910, 911737] |
75 |
C75 |
20) |
[8, 1938, 938953] |
[1] |
1 |
[8, 1938, 938953] |
75 |
C75 |
21) |
[8, 1602, 617401] |
[1] |
1 |
[8, 1602, 617401] |
75 |
C75 |
22) |
[8, 1526, 574969] |
[1] |
1 |
[8, 1526, 574969] |
75 |
C75 |
23) |
[8, 1366, 465337] |
[1] |
1 |
[8, 1366, 465337] |
75 |
C75 |
24) |
[8, 1062, 205129] |
[1] |
1 |
[8, 1062, 205129] |
75 |
C75 |
25) |
[8, 1478, 538921] |
[1] |
1 |
[8, 1478, 538921] |
75 |
C75 |
26) |
[8, 398, 38449] |
[1] |
1 |
[8, 398, 38449] |
75 |
C75 |
27) |
[5, 1017, 236461] |
[1] |
1 |
[5, 1017, 236461] |
75 |
C75 |
28) |
[5, 468, 54676] |
[1] |
2 |
[5, 468, 54676] |
150 |
C150 |
29) |
[5, 1821, 825229] |
[1] |
1 |
[5, 1821, 825229] |
75 |
C5 x C15 |
30) |
[5, 1461, 507349] |
[1] |
1 |
[5, 1461, 507349] |
75 |
C75 |
31) |
[5, 1641, 651109] |
[1] |
1 |
[5, 1641, 651109] |
75 |
C75 |
32) |
[5, 1457, 486061] |
[1] |
1 |
[5, 1457, 486061] |
75 |
C75 |
33) |
[5, 1929, 930229] |
[1] |
1 |
[5, 1929, 930229] |
75 |
C75 |
34) |
[5, 1729, 744829] |
[1] |
1 |
[5, 1729, 744829] |
75 |
C75 |
35) |
[5, 1677, 685381] |
[1] |
1 |
[5, 1677, 685381] |
75 |
C75 |
36) |
[5, 1721, 739909] |
[1] |
1 |
[5, 1721, 739909] |
75 |
C75 |
37) |
[5, 1769, 775309] |
[1] |
1 |
[5, 1769, 775309] |
75 |
C75 |
38) |
[5, 193, 9281] |
[5, 5] |
1 |
[5, 193, 9281] |
15 |
C15 |
39) |
[5, 613, 84481] |
[1] |
1 |
[5, 613, 84481] |
75 |
C75 |
40) |
[5, 1921, 922549] |
[1] |
1 |
[5, 1921, 922549] |
75 |
C5 x C15 |
41) |
[5, 1197, 315421] |
[1] |
1 |
[5, 1197, 315421] |
75 |
C75 |
42) |
[29, 252, 15412] |
[1] |
2 |
[29, 252, 15412] |
150 |
C5 x C30 |
43) |
[149, 157, 4337] |
[1] |
1 |
[149, 157, 4337] |
75 |
C75 |
44) |
[113, 783, 90868] |
[1] |
1 |
[113, 783, 90868] |
75 |
C75 |
45) |
[1229, 965, 8821] |
[1] |
1 |
[1229, 965, 8821] |
225 |
C3 x C75 |
46) |
[89, 1399, 431428] |
[1] |
1 |
[89, 1399, 431428] |
75 |
C5 x C15 |
47) |
[89, 1070, 170881] |
[1] |
1 |
[89, 1070, 170881] |
75 |
C75 |
48) |
[53, 513, 28573] |
[1] |
1 |
[53, 513, 28573] |
75 |
C75 |
49) |
[281, 679, 114628] |
[1] |
1 |
[281, 679, 114628] |
75 |
C75 |
50) |
[281, 1119, 216868] |
[1] |
1 |
[281, 1119, 216868] |
75 |
C75 |
51) |
[61, 181, 8053] |
[1] |
1 |
[61, 181, 8053] |
75 |
C75 |
52) |
[197, 741, 28477] |
[1] |
1 |
[197, 741, 28477] |
75 |
C75 |
53) |
[3209, 335, 20836] |
[1] |
1 |
[3209, 335, 20836] |
75 |
C75 |
54) |
[17, 1710, 717697] |
[1] |
1 |
[17, 1710, 717697] |
75 |
C75 |
55) |
[17, 434, 46477] |
[1] |
1 |
[17, 434, 46477] |
75 |
C75 |
56) |
[17, 1391, 479092] |
[1] |
1 |
[17, 1391, 479092] |
75 |
C75 |
57) |
[17, 1630, 661777] |
[1] |
1 |
[17, 1630, 661777] |
75 |
C75 |
58) |
[17, 831, 163252] |
[1] |
1 |
[17, 831, 163252] |
75 |
C5 x C15 |
59) |
[1777, 491, 6516] |
[1] |
1 |
[1777, 491, 6516] |
75 |
C75 |
60) |
[181, 141, 2753] |
[1] |
1 |
[181, 141, 2753] |
75 |
C75 |
61) |
[44, 348, 25876] |
[1] |
2 |
[44, 348, 25876] |
150 |
C150 |
62) |
[44, 302, 19237] |
[1] |
2 |
[44, 302, 19237] |
150 |
C150 |
63) |
[44, 446, 49333] |
[1] |
2 |
[44, 446, 49333] |
150 |
C150 |
64) |
[73, 102, 1433] |
[2, 2] |
1 |
[73, 102, 1433] |
75 |
C75 |
65) |
[73, 102, 1433] |
[1] |
1 |
[73, 102, 1433] |
75 |
C75 |
66) |
[41, 1615, 625396] |
[1] |
2 |
[41, 1615, 625396] |
150 |
C150 |
67) |
[41, 1919, 920548] |
[1] |
1 |
[41, 1919, 920548] |
75 |
C75 |
68) |
[929, 999, 26308] |
[1] |
1 |
[929, 999, 26308] |
75 |
C5 x C15 |