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 176 Igusa CM invariants of non-normal (D4) fields: 90
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[344, 444, 43780] |
[1] |
2 |
[344, 444, 43780] |
176 |
C2 x C2 x C44 |
2) |
[437, 345, 11293] |
[1] |
1 |
[437, 345, 11293] |
88 |
C88 |
3) |
[737, 255, 7228] |
[1] |
1 |
[737, 255, 7228] |
88 |
C2 x C44 |
4) |
[269, 369, 14605] |
[1] |
1 |
[269, 369, 14605] |
88 |
C2 x C44 |
5) |
[269, 753, 39465] |
[1] |
2 |
[269, 753, 39465] |
176 |
C2 x C88 |
6) |
[88, 100, 1708] |
[1] |
1 |
[88, 100, 1708] |
88 |
C2 x C44 |
7) |
[88, 442, 41713] |
[1] |
1 |
[88, 442, 41713] |
88 |
C2 x C44 |
8) |
[296, 492, 59332] |
[1] |
1 |
[296, 492, 59332] |
352 |
C2 x C4 x C44 |
9) |
[129, 382, 34417] |
[1] |
1 |
[129, 382, 34417] |
88 |
C88 |
10) |
[1033, 127, 1708] |
[1] |
1 |
[1033, 127, 1708] |
88 |
C2 x C44 |
11) |
[473, 327, 6748] |
[1] |
1 |
[473, 327, 6748] |
264 |
C2 x C132 |
12) |
[109, 686, 6033] |
[1] |
1 |
[109, 686, 6033] |
88 |
C88 |
13) |
[109, 373, 22765] |
[1] |
1 |
[109, 373, 22765] |
88 |
C2 x C44 |
14) |
[641, 287, 7612] |
[1] |
1 |
[641, 287, 7612] |
88 |
C2 x C44 |
15) |
[97, 571, 70816] |
[1] |
1 |
[97, 571, 70816] |
88 |
C88 |
16) |
[97, 287, 13584] |
[1] |
1 |
[97, 287, 13584] |
88 |
C88 |
17) |
[2381, 745, 4825] |
[1] |
2 |
[2381, 745, 4825] |
176 |
C2 x C88 |
18) |
[380, 456, 51604] |
[1] |
2 |
[380, 456, 51604] |
352 |
C2 x C4 x C44 |
19) |
[421, 433, 45925] |
[1] |
1 |
[421, 433, 45925] |
88 |
C88 |
20) |
[493, 961, 23697] |
[1] |
1 |
[493, 961, 23697] |
176 |
C176 |
21) |
[13, 529, 69229] |
[1] |
1 |
[13, 529, 69229] |
88 |
C88 |
22) |
[13, 565, 78373] |
[1] |
1 |
[13, 565, 78373] |
88 |
C88 |
23) |
[13, 1094, 282361] |
[1] |
1 |
[13, 1094, 282361] |
88 |
C88 |
24) |
[13, 469, 46537] |
[1] |
1 |
[13, 469, 46537] |
88 |
C88 |
25) |
[76, 304, 22420] |
[1] |
2 |
[76, 304, 22420] |
176 |
C2 x C2 x C44 |
26) |
[76, 322, 14977] |
[1] |
1 |
[76, 322, 14977] |
88 |
C2 x C44 |
27) |
[5, 1781, 775289] |
[1] |
1 |
[5, 1781, 775289] |
88 |
C88 |
28) |
[5, 1126, 281689] |
[1] |
1 |
[5, 1126, 281689] |
88 |
C88 |
29) |
[5, 1133, 309641] |
[1] |
1 |
[5, 1133, 309641] |
88 |
C88 |
30) |
[5, 1209, 312889] |
[1] |
1 |
[5, 1209, 312889] |
88 |
C88 |
31) |
[5, 1841, 846409] |
[1] |
1 |
[5, 1841, 846409] |
88 |
C88 |
32) |
[5, 897, 173401] |
[1] |
1 |
[5, 897, 173401] |
88 |
C88 |
33) |
[29, 445, 22529] |
[1] |
1 |
[29, 445, 22529] |
88 |
C88 |
34) |
[29, 429, 13465] |
[1] |
1 |
[29, 429, 13465] |
88 |
C88 |
35) |
[29, 1073, 65801] |
[1] |
1 |
[29, 1073, 65801] |
88 |
C88 |
36) |
[29, 462, 45937] |
[1] |
1 |
[29, 462, 45937] |
88 |
C88 |
37) |
[92, 474, 50281] |
[1] |
1 |
[92, 474, 50281] |
88 |
C2 x C44 |
38) |
[92, 446, 46417] |
[1] |
1 |
[92, 446, 46417] |
88 |
C2 x C44 |
39) |
[2117, 905, 115313] |
[1] |
1 |
[2117, 905, 115313] |
176 |
C176 |
40) |
[757, 1525, 526713] |
[1] |
1 |
[757, 1525, 526713] |
88 |
C88 |
41) |
[257, 407, 26956] |
[1] |
1 |
[257, 407, 26956] |
264 |
C2 x C132 |
42) |
[781, 957, 205337] |
[1] |
1 |
[781, 957, 205337] |
88 |
C88 |
43) |
[893, 1121, 99617] |
[1] |
1 |
[893, 1121, 99617] |
88 |
C2 x C44 |
44) |
[152, 444, 39556] |
[1] |
2 |
[152, 444, 39556] |
176 |
C2 x C2 x C44 |
45) |
[40, 466, 53929] |
[1] |
1 |
[40, 466, 53929] |
176 |
C2 x C2 x C44 |
46) |
[149, 561, 77749] |
[1] |
1 |
[149, 561, 77749] |
88 |
C2 x C44 |
47) |
[149, 318, 15745] |
[1] |
1 |
[149, 318, 15745] |
88 |
C2 x C44 |
48) |
[185, 471, 47644] |
[1] |
1 |
[185, 471, 47644] |
176 |
C4 x C44 |
49) |
[857, 207, 5356] |
[1] |
1 |
[857, 207, 5356] |
88 |
C2 x C44 |
50) |
[305, 471, 51724] |
[1] |
1 |
[305, 471, 51724] |
176 |
C4 x C44 |
51) |
[565, 345, 26225] |
[1] |
1 |
[565, 345, 26225] |
176 |
C176 |
52) |
[53, 168, 1756] |
[1] |
1 |
[53, 168, 1756] |
88 |
C88 |
53) |
[53, 790, 33913] |
[1] |
1 |
[53, 790, 33913] |
88 |
C88 |
54) |
[53, 414, 29281] |
[1] |
1 |
[53, 414, 29281] |
88 |
C2 x C44 |
55) |
[53, 689, 40121] |
[1] |
1 |
[53, 689, 40121] |
88 |
C88 |
56) |
[53, 222, 11473] |
[1] |
1 |
[53, 222, 11473] |
88 |
C2 x C44 |
57) |
[53, 777, 15769] |
[1] |
1 |
[53, 777, 15769] |
88 |
C88 |
58) |
[53, 621, 96397] |
[1] |
1 |
[53, 621, 96397] |
88 |
C2 x C44 |
59) |
[37, 1501, 524169] |
[1] |
1 |
[37, 1501, 524169] |
88 |
C88 |
60) |
[581, 333, 20605] |
[1] |
1 |
[581, 333, 20605] |
88 |
C2 x C44 |
61) |
[197, 369, 16261] |
[1] |
1 |
[197, 369, 16261] |
88 |
C2 x C44 |
62) |
[17, 359, 27592] |
[1] |
1 |
[17, 359, 27592] |
88 |
C88 |
63) |
[677, 269, 4381] |
[1] |
1 |
[677, 269, 4381] |
88 |
C88 |
64) |
[173, 71, 871] |
[1] |
1 |
[173, 71, 871] |
88 |
C2 x C44 |
65) |
[173, 429, 30397] |
[1] |
1 |
[173, 429, 30397] |
88 |
C88 |
66) |
[3373, 349, 9369] |
[1] |
1 |
[3373, 349, 9369] |
88 |
C88 |
67) |
[869, 201, 4669] |
[1] |
1 |
[869, 201, 4669] |
88 |
C2 x C44 |
68) |
[133, 361, 17917] |
[1] |
1 |
[133, 361, 17917] |
88 |
C2 x C44 |
69) |
[524, 368, 29140] |
[1] |
2 |
[524, 368, 29140] |
176 |
C2 x C2 x C44 |
70) |
[776, 242, 7657] |
[1] |
1 |
[776, 242, 7657] |
176 |
C4 x C44 |
71) |
[668, 296, 15892] |
[1] |
2 |
[668, 296, 15892] |
176 |
C4 x C44 |
72) |
[389, 341, 7189] |
[1] |
1 |
[389, 341, 7189] |
88 |
C2 x C44 |
73) |
[21, 577, 82597] |
[1] |
1 |
[21, 577, 82597] |
88 |
C88 |
74) |
[85, 265, 17365] |
[1] |
1 |
[85, 265, 17365] |
176 |
C4 x C44 |
75) |
[749, 261, 12349] |
[1] |
1 |
[749, 261, 12349] |
88 |
C2 x C44 |
76) |
[277, 717, 23193] |
[1] |
1 |
[277, 717, 23193] |
88 |
C88 |
77) |
[3221, 433, 39625] |
[1] |
1 |
[3221, 433, 39625] |
264 |
C264 |
78) |
[73, 391, 30172] |
[1] |
1 |
[73, 391, 30172] |
88 |
C2 x C44 |
79) |
[233, 507, 61408] |
[1] |
1 |
[233, 507, 61408] |
88 |
C2 x C44 |
80) |
[56, 602, 90097] |
[1] |
1 |
[56, 602, 90097] |
88 |
C2 x C44 |
81) |
[1889, 45, 34] |
[1] |
1 |
[1889, 45, 34] |
88 |
C88 |
82) |
[41, 643, 48740] |
[1] |
1 |
[41, 643, 48740] |
88 |
C88 |
83) |
[241, 955, 18276] |
[1] |
1 |
[241, 955, 18276] |
88 |
C88 |
84) |
[829, 1021, 6729] |
[1] |
1 |
[829, 1021, 6729] |
88 |
C88 |
85) |
[101, 1718, 712025] |
[1] |
1 |
[101, 1718, 712025] |
88 |
C88 |
86) |
[101, 1313, 396425] |
[1] |
1 |
[101, 1313, 396425] |
88 |
C88 |
87) |
[172, 286, 14257] |
[1] |
1 |
[172, 286, 14257] |
88 |
C88 |
88) |
[557, 309, 7021] |
[1] |
1 |
[557, 309, 7021] |
88 |
C2 x C44 |
89) |
[2341, 93, 1577] |
[1] |
1 |
[2341, 93, 1577] |
88 |
C88 |
90) |
[989, 153, 5605] |
[1] |
1 |
[989, 153, 5605] |
88 |
C2 x C44 |