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 280 Igusa CM invariants of non-normal (D4) fields: 127
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[165, 574, 16369] |
[1] |
1 |
[165, 574, 16369] |
280 |
C2 x C2 x C70 |
2) |
[344, 1014, 90553] |
[1] |
1 |
[344, 1014, 90553] |
140 |
C140 |
3) |
[157, 833, 164641] |
[1] |
1 |
[157, 833, 164641] |
140 |
C2 x C70 |
4) |
[237, 593, 50881] |
[1] |
1 |
[237, 593, 50881] |
140 |
C2 x C70 |
5) |
[1117, 425, 22537] |
[1] |
1 |
[1117, 425, 22537] |
140 |
C140 |
6) |
[437, 541, 15377] |
[1] |
1 |
[437, 541, 15377] |
140 |
C140 |
7) |
[60, 566, 39529] |
[1] |
1 |
[60, 566, 39529] |
280 |
C2 x C140 |
8) |
[60, 626, 63409] |
[1] |
1 |
[60, 626, 63409] |
280 |
C2 x C2 x C70 |
9) |
[60, 866, 183649] |
[1] |
1 |
[60, 866, 183649] |
280 |
C2 x C140 |
10) |
[60, 662, 80521] |
[1] |
1 |
[60, 662, 80521] |
280 |
C2 x C140 |
11) |
[885, 469, 5209] |
[1] |
1 |
[885, 469, 5209] |
280 |
C2 x C140 |
12) |
[229, 421, 31429] |
[1] |
1 |
[229, 421, 31429] |
420 |
C420 |
13) |
[301, 561, 31649] |
[1] |
1 |
[301, 561, 31649] |
140 |
C140 |
14) |
[805, 509, 19489] |
[1] |
1 |
[805, 509, 19489] |
280 |
C2 x C2 x C70 |
15) |
[137, 1035, 210232] |
[1] |
1 |
[137, 1035, 210232] |
140 |
C2 x C70 |
16) |
[88, 530, 31417] |
[1] |
1 |
[88, 530, 31417] |
140 |
C2 x C70 |
17) |
[120, 542, 15361] |
[1] |
1 |
[120, 542, 15361] |
280 |
C2 x C2 x C70 |
18) |
[120, 178, 6841] |
[1] |
1 |
[120, 178, 6841] |
280 |
C2 x C2 x C70 |
19) |
[665, 1247, 267556] |
[1] |
1 |
[665, 1247, 267556] |
280 |
C2 x C140 |
20) |
[665, 582, 42121] |
[1] |
1 |
[665, 582, 42121] |
280 |
C2 x C140 |
21) |
[357, 302, 17089] |
[1] |
1 |
[357, 302, 17089] |
280 |
C2 x C140 |
22) |
[104, 574, 32033] |
[1] |
1 |
[104, 574, 32033] |
280 |
C2 x C2 x C70 |
23) |
[312, 530, 17497] |
[1] |
1 |
[312, 530, 17497] |
280 |
C2 x C2 x C70 |
24) |
[109, 965, 232561] |
[1] |
1 |
[109, 965, 232561] |
140 |
C140 |
25) |
[309, 398, 34657] |
[1] |
1 |
[309, 398, 34657] |
140 |
C140 |
26) |
[1501, 1189, 350053] |
[1] |
1 |
[1501, 1189, 350053] |
140 |
C140 |
27) |
[136, 186, 8513] |
[1] |
1 |
[136, 186, 8513] |
280 |
C2 x C140 |
28) |
[209, 1238, 262777] |
[1] |
1 |
[209, 1238, 262777] |
140 |
C140 |
29) |
[13, 601, 68977] |
[1] |
1 |
[13, 601, 68977] |
140 |
C140 |
30) |
[13, 993, 246353] |
[1] |
1 |
[13, 993, 246353] |
140 |
C140 |
31) |
[8, 874, 185969] |
[1] |
1 |
[8, 874, 185969] |
140 |
C2 x C70 |
32) |
[8, 826, 164737] |
[1] |
1 |
[8, 826, 164737] |
140 |
C140 |
33) |
[8, 862, 183169] |
[1] |
1 |
[8, 862, 183169] |
140 |
C2 x C70 |
34) |
[5, 1737, 743941] |
[1] |
1 |
[5, 1737, 743941] |
140 |
C140 |
35) |
[5, 1542, 555721] |
[1] |
1 |
[5, 1542, 555721] |
140 |
C140 |
36) |
[29, 629, 64393] |
[1] |
1 |
[29, 629, 64393] |
140 |
C140 |
37) |
[29, 1709, 726973] |
[1] |
1 |
[29, 1709, 726973] |
140 |
C140 |
38) |
[29, 749, 121393] |
[1] |
1 |
[29, 749, 121393] |
140 |
C140 |
39) |
[29, 577, 52601] |
[1] |
1 |
[29, 577, 52601] |
140 |
C140 |
40) |
[29, 893, 199297] |
[1] |
1 |
[29, 893, 199297] |
140 |
C2 x C70 |
41) |
[29, 829, 169193] |
[1] |
1 |
[29, 829, 169193] |
140 |
C140 |
42) |
[92, 1182, 242929] |
[1] |
1 |
[92, 1182, 242929] |
140 |
C140 |
43) |
[124, 458, 47977] |
[1] |
1 |
[124, 458, 47977] |
140 |
C140 |
44) |
[124, 534, 11273] |
[1] |
1 |
[124, 534, 11273] |
140 |
C140 |
45) |
[124, 730, 61801] |
[1] |
1 |
[124, 730, 61801] |
140 |
C2 x C70 |
46) |
[124, 614, 54073] |
[1] |
1 |
[124, 614, 54073] |
140 |
C2 x C70 |
47) |
[124, 450, 18881] |
[1] |
1 |
[124, 450, 18881] |
140 |
C2 x C70 |
48) |
[93, 893, 195433] |
[1] |
1 |
[93, 893, 195433] |
140 |
C140 |
49) |
[93, 565, 62857] |
[1] |
1 |
[93, 565, 62857] |
140 |
C2 x C70 |
50) |
[93, 493, 13681] |
[1] |
1 |
[93, 493, 13681] |
140 |
C140 |
51) |
[93, 550, 22057] |
[1] |
1 |
[93, 550, 22057] |
140 |
C2 x C70 |
52) |
[24, 670, 81121] |
[1] |
1 |
[24, 670, 81121] |
140 |
C2 x C70 |
53) |
[24, 1690, 711121] |
[1] |
1 |
[24, 1690, 711121] |
140 |
C140 |
54) |
[24, 418, 33097] |
[1] |
1 |
[24, 418, 33097] |
140 |
C2 x C70 |
55) |
[24, 818, 156697] |
[1] |
1 |
[24, 818, 156697] |
140 |
C2 x C70 |
56) |
[24, 734, 123073] |
[1] |
1 |
[24, 734, 123073] |
140 |
C2 x C70 |
57) |
[24, 674, 109513] |
[1] |
1 |
[24, 674, 109513] |
140 |
C2 x C70 |
58) |
[24, 922, 163921] |
[1] |
1 |
[24, 922, 163921] |
140 |
C2 x C70 |
59) |
[221, 601, 55769] |
[1] |
1 |
[221, 601, 55769] |
280 |
C2 x C140 |
60) |
[1549, 245, 11521] |
[1] |
1 |
[1549, 245, 11521] |
140 |
C140 |
61) |
[285, 422, 26281] |
[1] |
1 |
[285, 422, 26281] |
280 |
C2 x C2 x C70 |
62) |
[285, 446, 45169] |
[1] |
1 |
[285, 446, 45169] |
280 |
C2 x C140 |
63) |
[105, 619, 79384] |
[1] |
1 |
[105, 619, 79384] |
280 |
C2 x C140 |
64) |
[141, 710, 117001] |
[1] |
1 |
[141, 710, 117001] |
140 |
C2 x C70 |
65) |
[141, 769, 69973] |
[1] |
1 |
[141, 769, 69973] |
140 |
C2 x C70 |
66) |
[152, 322, 13609] |
[1] |
1 |
[152, 322, 13609] |
140 |
C2 x C70 |
67) |
[40, 842, 176881] |
[1] |
1 |
[40, 842, 176881] |
280 |
C2 x C2 x C70 |
68) |
[40, 926, 212929] |
[1] |
1 |
[40, 926, 212929] |
280 |
C2 x C2 x C70 |
69) |
[185, 1062, 92521] |
[1] |
1 |
[185, 1062, 92521] |
280 |
C2 x C140 |
70) |
[185, 389, 37414] |
[1] |
1 |
[185, 389, 37414] |
280 |
C2 x C140 |
71) |
[156, 550, 25081] |
[1] |
1 |
[156, 550, 25081] |
280 |
C2 x C140 |
72) |
[53, 673, 86401] |
[1] |
1 |
[53, 673, 86401] |
140 |
C140 |
73) |
[957, 461, 12697] |
[1] |
1 |
[957, 461, 12697] |
280 |
C2 x C2 x C70 |
74) |
[37, 857, 183529] |
[1] |
1 |
[37, 857, 183529] |
140 |
C140 |
75) |
[37, 797, 148729] |
[1] |
1 |
[37, 797, 148729] |
140 |
C140 |
76) |
[789, 545, 40921] |
[1] |
1 |
[789, 545, 40921] |
140 |
C140 |
77) |
[364, 554, 24313] |
[1] |
1 |
[364, 554, 24313] |
280 |
C2 x C140 |
78) |
[28, 778, 115033] |
[1] |
1 |
[28, 778, 115033] |
140 |
C140 |
79) |
[28, 866, 183457] |
[1] |
1 |
[28, 866, 183457] |
140 |
C2 x C70 |
80) |
[28, 630, 80297] |
[1] |
1 |
[28, 630, 80297] |
140 |
C2 x C70 |
81) |
[28, 618, 89993] |
[1] |
1 |
[28, 618, 89993] |
140 |
C2 x C70 |
82) |
[28, 782, 148849] |
[1] |
1 |
[28, 782, 148849] |
140 |
C2 x C70 |
83) |
[28, 498, 54833] |
[1] |
1 |
[28, 498, 54833] |
140 |
C140 |
84) |
[204, 530, 30241] |
[1] |
1 |
[204, 530, 30241] |
280 |
C2 x C2 x C70 |
85) |
[33, 1447, 488596] |
[1] |
1 |
[33, 1447, 488596] |
140 |
C140 |
86) |
[61, 953, 225817] |
[1] |
1 |
[61, 953, 225817] |
140 |
C140 |
87) |
[61, 397, 32677] |
[1] |
1 |
[61, 397, 32677] |
140 |
C140 |
88) |
[541, 641, 72289] |
[1] |
1 |
[541, 641, 72289] |
140 |
C2 x C70 |
89) |
[1101, 413, 9337] |
[1] |
1 |
[1101, 413, 9337] |
420 |
C420 |
90) |
[1085, 421, 11489] |
[1] |
1 |
[1085, 421, 11489] |
280 |
C2 x C140 |
91) |
[593, 963, 28888] |
[1] |
1 |
[593, 963, 28888] |
140 |
C2 x C70 |
92) |
[881, 1239, 267268] |
[1] |
1 |
[881, 1239, 267268] |
140 |
C140 |
93) |
[17, 478, 56033] |
[1] |
1 |
[17, 478, 56033] |
140 |
C140 |
94) |
[173, 521, 64357] |
[1] |
1 |
[173, 521, 64357] |
140 |
C140 |
95) |
[1644, 194, 2833] |
[1] |
1 |
[1644, 194, 2833] |
280 |
C2 x C2 x C70 |
96) |
[133, 385, 12817] |
[1] |
1 |
[133, 385, 12817] |
140 |
C140 |
97) |
[77, 721, 119777] |
[1] |
1 |
[77, 721, 119777] |
140 |
C2 x C70 |
98) |
[44, 442, 31241] |
[1] |
1 |
[44, 442, 31241] |
140 |
C2 x C70 |
99) |
[44, 1850, 854041] |
[1] |
1 |
[44, 1850, 854041] |
140 |
C140 |
100) |
[44, 970, 234521] |
[1] |
1 |
[44, 970, 234521] |
140 |
C2 x C70 |
101) |
[44, 886, 191849] |
[1] |
1 |
[44, 886, 191849] |
140 |
C2 x C70 |
102) |
[12, 758, 132841] |
[1] |
1 |
[12, 758, 132841] |
140 |
C2 x C70 |
103) |
[12, 1426, 492817] |
[1] |
1 |
[12, 1426, 492817] |
140 |
C2 x C70 |
104) |
[12, 998, 248953] |
[1] |
1 |
[12, 998, 248953] |
140 |
C2 x C70 |
105) |
[21, 925, 213481] |
[1] |
1 |
[21, 925, 213481] |
140 |
C140 |
106) |
[21, 1429, 470773] |
[1] |
1 |
[21, 1429, 470773] |
140 |
C2 x C70 |
107) |
[21, 677, 92401] |
[1] |
1 |
[21, 677, 92401] |
140 |
C140 |
108) |
[21, 1705, 713101] |
[1] |
1 |
[21, 1705, 713101] |
140 |
C2 x C70 |
109) |
[741, 509, 11233] |
[1] |
1 |
[741, 509, 11233] |
280 |
C2 x C140 |
110) |
[56, 610, 52201] |
[1] |
1 |
[56, 610, 52201] |
140 |
C140 |
111) |
[56, 418, 27497] |
[1] |
1 |
[56, 418, 27497] |
140 |
C2 x C70 |
112) |
[713, 510, 53617] |
[1] |
1 |
[713, 510, 53617] |
140 |
C140 |
113) |
[201, 1150, 173041] |
[1] |
1 |
[201, 1150, 173041] |
140 |
C2 x C70 |
114) |
[201, 739, 25528] |
[1] |
1 |
[201, 739, 25528] |
140 |
C2 x C70 |
115) |
[241, 811, 42424] |
[1] |
1 |
[241, 811, 42424] |
140 |
C140 |
116) |
[397, 222, 5969] |
[1] |
1 |
[397, 222, 5969] |
140 |
C140 |
117) |
[284, 406, 12809] |
[1] |
1 |
[284, 406, 12809] |
140 |
C140 |
118) |
[424, 714, 106673] |
[1] |
1 |
[424, 714, 106673] |
280 |
C2 x C2 x C70 |
119) |
[3009, 415, 6196] |
[1] |
1 |
[3009, 415, 6196] |
280 |
C2 x C2 x C70 |
120) |
[1133, 397, 5129] |
[1] |
1 |
[1133, 397, 5129] |
140 |
C140 |
121) |
[1356, 314, 2953] |
[1] |
1 |
[1356, 314, 2953] |
280 |
C2 x C2 x C70 |
122) |
[904, 522, 45521] |
[1] |
1 |
[904, 522, 45521] |
1120 |
C2 x C560 |
123) |
[69, 809, 157393] |
[1] |
1 |
[69, 809, 157393] |
140 |
C140 |
124) |
[69, 689, 111073] |
[1] |
1 |
[69, 689, 111073] |
140 |
C140 |
125) |
[69, 445, 30721] |
[1] |
1 |
[69, 445, 30721] |
140 |
C140 |
126) |
[69, 845, 173521] |
[1] |
1 |
[69, 845, 173521] |
140 |
C2 x C70 |
127) |
[1309, 365, 30361] |
[1] |
1 |
[1309, 365, 30361] |
280 |
C2 x C140 |