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 352 Igusa CM invariants of non-normal (D4) fields: 94
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[2437, 745, 35793] |
[1] |
1 |
[2437, 745, 35793] |
176 |
C176 |
2) |
[317, 489, 59701] |
[1] |
1 |
[317, 489, 59701] |
176 |
C176 |
3) |
[157, 1969, 969201] |
[1] |
1 |
[157, 1969, 969201] |
176 |
C176 |
4) |
[157, 79, 1207] |
[1] |
1 |
[157, 79, 1207] |
176 |
C4 x C44 |
5) |
[3109, 493, 59985] |
[1] |
1 |
[3109, 493, 59985] |
176 |
C2 x C88 |
6) |
[1117, 1069, 50841] |
[1] |
1 |
[1117, 1069, 50841] |
176 |
C2 x C88 |
7) |
[229, 1302, 291897] |
[1] |
1 |
[229, 1302, 291897] |
528 |
C2 x C264 |
8) |
[301, 1717, 709857] |
[1] |
1 |
[301, 1717, 709857] |
176 |
C2 x C88 |
9) |
[269, 1913, 914825] |
[1] |
1 |
[269, 1913, 914825] |
176 |
C2 x C88 |
10) |
[269, 901, 66769] |
[1] |
1 |
[269, 901, 66769] |
176 |
C176 |
11) |
[236, 1574, 618425] |
[1] |
1 |
[236, 1574, 618425] |
176 |
C176 |
12) |
[349, 1861, 863649] |
[1] |
1 |
[349, 1861, 863649] |
176 |
C2 x C88 |
13) |
[120, 538, 69361] |
[1] |
1 |
[120, 538, 69361] |
352 |
C2 x C2 x C88 |
14) |
[461, 413, 41605] |
[1] |
1 |
[461, 413, 41605] |
176 |
C2 x C88 |
15) |
[213, 481, 51397] |
[1] |
1 |
[213, 481, 51397] |
176 |
C176 |
16) |
[161, 559, 39440] |
[1] |
1 |
[161, 559, 39440] |
176 |
C2 x C88 |
17) |
[109, 1126, 273369] |
[1] |
1 |
[109, 1126, 273369] |
176 |
C2 x C88 |
18) |
[109, 1438, 431505] |
[1] |
1 |
[109, 1438, 431505] |
176 |
C2 x C88 |
19) |
[813, 1461, 460257] |
[1] |
1 |
[813, 1461, 460257] |
176 |
C2 x C88 |
20) |
[797, 249, 15301] |
[1] |
1 |
[797, 249, 15301] |
176 |
C2 x C88 |
21) |
[97, 134, 2937] |
[1] |
1 |
[97, 134, 2937] |
176 |
C2 x C88 |
22) |
[733, 1137, 123633] |
[1] |
1 |
[733, 1137, 123633] |
528 |
C2 x C264 |
23) |
[205, 1041, 192969] |
[1] |
1 |
[205, 1041, 192969] |
352 |
C4 x C88 |
24) |
[1621, 133, 4017] |
[1] |
1 |
[1621, 133, 4017] |
176 |
C2 x C88 |
25) |
[2776, 642, 78057] |
[1] |
1 |
[2776, 642, 78057] |
176 |
C176 |
26) |
[209, 519, 64780] |
[1] |
1 |
[209, 519, 64780] |
176 |
C2 x C2 x C44 |
27) |
[13, 1585, 582033] |
[1] |
1 |
[13, 1585, 582033] |
176 |
C2 x C88 |
28) |
[13, 2017, 1016913] |
[1] |
1 |
[13, 2017, 1016913] |
176 |
C2 x C88 |
29) |
[8, 1102, 176593] |
[1] |
1 |
[8, 1102, 176593] |
176 |
C176 |
30) |
[5, 1558, 588841] |
[1] |
1 |
[5, 1558, 588841] |
176 |
C2 x C88 |
31) |
[5, 1438, 444961] |
[1] |
1 |
[5, 1438, 444961] |
176 |
C2 x C88 |
32) |
[29, 1661, 680849] |
[1] |
1 |
[29, 1661, 680849] |
176 |
C2 x C88 |
33) |
[941, 1033, 10585] |
[1] |
1 |
[941, 1033, 10585] |
176 |
C2 x C88 |
34) |
[2749, 649, 71625] |
[1] |
1 |
[2749, 649, 71625] |
176 |
C2 x C88 |
35) |
[440, 378, 24721] |
[1] |
1 |
[440, 378, 24721] |
352 |
C2 x C2 x C88 |
36) |
[93, 1617, 648441] |
[1] |
1 |
[93, 1617, 648441] |
176 |
C2 x C88 |
37) |
[93, 589, 86149] |
[1] |
1 |
[93, 589, 86149] |
176 |
C2 x C88 |
38) |
[93, 1214, 247921] |
[1] |
1 |
[93, 1214, 247921] |
176 |
C2 x C88 |
39) |
[93, 601, 90277] |
[1] |
1 |
[93, 601, 90277] |
176 |
C2 x C88 |
40) |
[24, 1586, 580249] |
[1] |
1 |
[24, 1586, 580249] |
176 |
C176 |
41) |
[24, 1586, 623449] |
[1] |
1 |
[24, 1586, 623449] |
176 |
C176 |
42) |
[221, 1574, 605225] |
[1] |
1 |
[221, 1574, 605225] |
352 |
C4 x C88 |
43) |
[877, 205, 8533] |
[1] |
1 |
[877, 205, 8533] |
176 |
C2 x C88 |
44) |
[285, 481, 54349] |
[1] |
1 |
[285, 481, 54349] |
352 |
C4 x C88 |
45) |
[105, 583, 84316] |
[1] |
1 |
[105, 583, 84316] |
352 |
C4 x C88 |
46) |
[1333, 1069, 77409] |
[1] |
1 |
[1333, 1069, 77409] |
176 |
C2 x C88 |
47) |
[152, 570, 81073] |
[1] |
1 |
[152, 570, 81073] |
176 |
C4 x C44 |
48) |
[149, 961, 155449] |
[1] |
1 |
[149, 961, 155449] |
176 |
C2 x C88 |
49) |
[1541, 1165, 252625] |
[1] |
1 |
[1541, 1165, 252625] |
176 |
C2 x C88 |
50) |
[53, 1541, 580937] |
[1] |
1 |
[53, 1541, 580937] |
176 |
C2 x C88 |
51) |
[53, 721, 95497] |
[1] |
1 |
[53, 721, 95497] |
176 |
C2 x C88 |
52) |
[957, 169, 6901] |
[1] |
1 |
[957, 169, 6901] |
352 |
C2 x C2 x C88 |
53) |
[1909, 117, 2945] |
[1] |
1 |
[1909, 117, 2945] |
176 |
C2 x C88 |
54) |
[2236, 898, 165825] |
[1] |
1 |
[2236, 898, 165825] |
352 |
C2 x C176 |
55) |
[37, 2005, 1004553] |
[1] |
1 |
[37, 2005, 1004553] |
176 |
C2 x C88 |
56) |
[37, 409, 37741] |
[1] |
1 |
[37, 409, 37741] |
176 |
C2 x C88 |
57) |
[364, 394, 25705] |
[1] |
1 |
[364, 394, 25705] |
352 |
C4 x C88 |
58) |
[293, 489, 57949] |
[1] |
1 |
[293, 489, 57949] |
176 |
C176 |
59) |
[465, 391, 32524] |
[1] |
1 |
[465, 391, 32524] |
352 |
C4 x C88 |
60) |
[537, 966, 224697] |
[1] |
1 |
[537, 966, 224697] |
176 |
C176 |
61) |
[501, 373, 28645] |
[1] |
1 |
[501, 373, 28645] |
176 |
C2 x C88 |
62) |
[33, 803, 121924] |
[1] |
1 |
[33, 803, 121924] |
176 |
C2 x C88 |
63) |
[61, 1201, 296169] |
[1] |
1 |
[61, 1201, 296169] |
176 |
C2 x C88 |
64) |
[61, 1409, 396265] |
[1] |
1 |
[61, 1409, 396265] |
176 |
C2 x C88 |
65) |
[61, 1661, 658849] |
[1] |
1 |
[61, 1661, 658849] |
176 |
C176 |
66) |
[61, 1257, 371817] |
[1] |
1 |
[61, 1257, 371817] |
176 |
C2 x C88 |
67) |
[1101, 1385, 417625] |
[1] |
1 |
[1101, 1385, 417625] |
528 |
C2 x C264 |
68) |
[677, 297, 17821] |
[1] |
1 |
[677, 297, 17821] |
176 |
C176 |
69) |
[173, 294, 18841] |
[1] |
1 |
[173, 294, 18841] |
176 |
C176 |
70) |
[2069, 1009, 249865] |
[1] |
1 |
[2069, 1009, 249865] |
176 |
C2 x C88 |
71) |
[232, 370, 15433] |
[1] |
1 |
[232, 370, 15433] |
352 |
C4 x C88 |
72) |
[133, 1437, 480033] |
[1] |
1 |
[133, 1437, 480033] |
176 |
C2 x C88 |
73) |
[77, 1094, 91001] |
[1] |
1 |
[77, 1094, 91001] |
176 |
C2 x C88 |
74) |
[77, 709, 75601] |
[1] |
1 |
[77, 709, 75601] |
176 |
C2 x C88 |
75) |
[1213, 1429, 502929] |
[1] |
1 |
[1213, 1429, 502929] |
176 |
C176 |
76) |
[21, 1382, 368617] |
[1] |
1 |
[21, 1382, 368617] |
176 |
C176 |
77) |
[21, 1277, 399697] |
[1] |
1 |
[21, 1277, 399697] |
176 |
C176 |
78) |
[21, 1534, 103105] |
[1] |
1 |
[21, 1534, 103105] |
176 |
C2 x C88 |
79) |
[21, 1718, 710665] |
[1] |
1 |
[21, 1718, 710665] |
176 |
C2 x C88 |
80) |
[85, 2005, 1004985] |
[1] |
1 |
[85, 2005, 1004985] |
352 |
C4 x C88 |
81) |
[277, 1689, 682641] |
[1] |
1 |
[277, 1689, 682641] |
176 |
C2 x C88 |
82) |
[1181, 1093, 83425] |
[1] |
1 |
[1181, 1093, 83425] |
176 |
C176 |
83) |
[485, 381, 30349] |
[1] |
1 |
[485, 381, 30349] |
352 |
C2 x C2 x C2 x C44 |
84) |
[1349, 1153, 183625] |
[1] |
1 |
[1349, 1153, 183625] |
176 |
C2 x C88 |
85) |
[829, 382, 23217] |
[1] |
1 |
[829, 382, 23217] |
176 |
C2 x C88 |
86) |
[2101, 997, 247977] |
[1] |
1 |
[2101, 997, 247977] |
528 |
C528 |
87) |
[397, 201, 10001] |
[1] |
1 |
[397, 201, 10001] |
176 |
C176 |
88) |
[397, 337, 6061] |
[1] |
1 |
[397, 337, 6061] |
176 |
C2 x C88 |
89) |
[365, 425, 37765] |
[1] |
1 |
[365, 425, 37765] |
352 |
C2 x C4 x C44 |
90) |
[472, 1474, 463401] |
[1] |
1 |
[472, 1474, 463401] |
176 |
C176 |
91) |
[101, 797, 98177] |
[1] |
1 |
[101, 797, 98177] |
176 |
C176 |
92) |
[557, 806, 19817] |
[1] |
1 |
[557, 806, 19817] |
176 |
C2 x C88 |
93) |
[2589, 749, 134425] |
[1] |
1 |
[2589, 749, 134425] |
528 |
C528 |
94) |
[717, 1005, 7113] |
[1] |
1 |
[717, 1005, 7113] |
176 |
C176 |