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 252 Igusa CM invariants of non-normal (D4) fields: 97
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[661, 581, 47209] |
[1] |
1 |
[661, 581, 47209] |
126 |
C126 |
2) |
[1853, 97, 1889] |
[1] |
1 |
[1853, 97, 1889] |
252 |
C2 x C126 |
3) |
[237, 518, 51913] |
[1] |
1 |
[237, 518, 51913] |
126 |
C126 |
4) |
[1237, 365, 8257] |
[1] |
1 |
[1237, 365, 8257] |
126 |
C3 x C42 |
5) |
[229, 765, 129761] |
[1] |
2 |
[229, 765, 129761] |
756 |
C6 x C126 |
6) |
[301, 653, 73417] |
[1] |
1 |
[301, 653, 73417] |
126 |
C126 |
7) |
[236, 454, 5273] |
[1] |
1 |
[236, 454, 5273] |
126 |
C126 |
8) |
[88, 318, 23873] |
[1] |
1 |
[88, 318, 23873] |
126 |
C126 |
9) |
[88, 402, 14969] |
[1] |
1 |
[88, 402, 14969] |
126 |
C126 |
10) |
[461, 681, 90009] |
[1] |
2 |
[461, 681, 90009] |
252 |
C2 x C126 |
11) |
[213, 653, 78433] |
[1] |
1 |
[213, 653, 78433] |
126 |
C126 |
12) |
[109, 509, 52753] |
[1] |
1 |
[109, 509, 52753] |
126 |
C126 |
13) |
[797, 513, 20961] |
[1] |
2 |
[797, 513, 20961] |
252 |
C2 x C126 |
14) |
[205, 701, 100249] |
[1] |
1 |
[205, 701, 100249] |
252 |
C252 |
15) |
[309, 605, 50641] |
[1] |
1 |
[309, 605, 50641] |
126 |
C126 |
16) |
[1765, 141, 4529] |
[1] |
1 |
[1765, 141, 4529] |
756 |
C3 x C252 |
17) |
[844, 474, 2153] |
[1] |
1 |
[844, 474, 2153] |
126 |
C126 |
18) |
[493, 557, 23209] |
[1] |
1 |
[493, 557, 23209] |
252 |
C2 x C126 |
19) |
[493, 665, 82825] |
[1] |
2 |
[493, 665, 82825] |
504 |
C2 x C2 x C126 |
20) |
[13, 1862, 597193] |
[1] |
1 |
[13, 1862, 597193] |
126 |
C126 |
21) |
[13, 1446, 392729] |
[1] |
1 |
[13, 1446, 392729] |
126 |
C126 |
22) |
[13, 2294, 566809] |
[1] |
1 |
[13, 2294, 566809] |
126 |
C126 |
23) |
[13, 2414, 1426897] |
[1] |
1 |
[13, 2414, 1426897] |
126 |
C126 |
24) |
[13, 2294, 948697] |
[1] |
1 |
[13, 2294, 948697] |
126 |
C126 |
25) |
[76, 534, 19913] |
[1] |
1 |
[76, 534, 19913] |
126 |
C126 |
26) |
[8, 878, 192433] |
[1] |
1 |
[8, 878, 192433] |
126 |
C126 |
27) |
[8, 1546, 472529] |
[1] |
1 |
[8, 1546, 472529] |
126 |
C126 |
28) |
[8, 970, 153617] |
[1] |
1 |
[8, 970, 153617] |
126 |
C126 |
29) |
[5, 3181, 2518409] |
[1] |
1 |
[5, 3181, 2518409] |
126 |
C126 |
30) |
[5, 1657, 679001] |
[1] |
1 |
[5, 1657, 679001] |
126 |
C126 |
31) |
[5, 1981, 975809] |
[1] |
1 |
[5, 1981, 975809] |
126 |
C126 |
32) |
[5, 1981, 954809] |
[1] |
1 |
[5, 1981, 954809] |
126 |
C126 |
33) |
[5, 1342, 442241] |
[1] |
1 |
[5, 1342, 442241] |
126 |
C126 |
34) |
[5, 2461, 1313129] |
[1] |
1 |
[5, 2461, 1313129] |
126 |
C126 |
35) |
[5, 2806, 1576409] |
[1] |
1 |
[5, 2806, 1576409] |
126 |
C126 |
36) |
[29, 809, 152593] |
[1] |
1 |
[29, 809, 152593] |
126 |
C126 |
37) |
[29, 697, 116921] |
[1] |
1 |
[29, 697, 116921] |
126 |
C126 |
38) |
[93, 605, 91297] |
[1] |
1 |
[93, 605, 91297] |
126 |
C126 |
39) |
[93, 593, 82681] |
[1] |
1 |
[93, 593, 82681] |
126 |
C126 |
40) |
[93, 710, 102217] |
[1] |
1 |
[93, 710, 102217] |
126 |
C126 |
41) |
[24, 734, 115873] |
[1] |
1 |
[24, 734, 115873] |
126 |
C126 |
42) |
[24, 926, 211969] |
[1] |
1 |
[24, 926, 211969] |
126 |
C126 |
43) |
[221, 550, 61481] |
[1] |
1 |
[221, 550, 61481] |
252 |
C252 |
44) |
[1141, 393, 4097] |
[1] |
1 |
[1141, 393, 4097] |
126 |
C126 |
45) |
[141, 614, 58153] |
[1] |
1 |
[141, 614, 58153] |
126 |
C126 |
46) |
[1816, 114, 1433] |
[1] |
1 |
[1816, 114, 1433] |
126 |
C126 |
47) |
[40, 794, 148609] |
[1] |
1 |
[40, 794, 148609] |
252 |
C2 x C126 |
48) |
[40, 986, 242689] |
[1] |
1 |
[40, 986, 242689] |
252 |
C2 x C126 |
49) |
[40, 606, 60449] |
[1] |
1 |
[40, 606, 60449] |
252 |
C2 x C126 |
50) |
[149, 529, 38633] |
[1] |
1 |
[149, 529, 38633] |
126 |
C126 |
51) |
[1832, 106, 977] |
[1] |
1 |
[1832, 106, 977] |
252 |
C2 x C126 |
52) |
[533, 537, 13329] |
[1] |
2 |
[533, 537, 13329] |
504 |
C2 x C2 x C126 |
53) |
[53, 605, 48457] |
[1] |
1 |
[53, 605, 48457] |
126 |
C126 |
54) |
[53, 733, 127313] |
[1] |
1 |
[53, 733, 127313] |
126 |
C126 |
55) |
[53, 853, 178073] |
[1] |
1 |
[53, 853, 178073] |
126 |
C126 |
56) |
[1189, 389, 13753] |
[1] |
1 |
[1189, 389, 13753] |
252 |
C252 |
57) |
[37, 558, 48833] |
[1] |
1 |
[37, 558, 48833] |
126 |
C126 |
58) |
[37, 726, 131177] |
[1] |
1 |
[37, 726, 131177] |
126 |
C126 |
59) |
[1477, 281, 16417] |
[1] |
1 |
[1477, 281, 16417] |
126 |
C126 |
60) |
[293, 305, 14393] |
[1] |
1 |
[293, 305, 14393] |
126 |
C126 |
61) |
[197, 505, 22337] |
[1] |
1 |
[197, 505, 22337] |
126 |
C126 |
62) |
[173, 245, 14617] |
[1] |
1 |
[173, 245, 14617] |
126 |
C126 |
63) |
[173, 365, 28073] |
[1] |
1 |
[173, 365, 28073] |
126 |
C3 x C42 |
64) |
[1676, 178, 1217] |
[1] |
1 |
[1676, 178, 1217] |
126 |
C126 |
65) |
[133, 737, 121129] |
[1] |
1 |
[133, 737, 121129] |
126 |
C126 |
66) |
[133, 593, 63673] |
[1] |
1 |
[133, 593, 63673] |
126 |
C126 |
67) |
[1261, 353, 5617] |
[1] |
1 |
[1261, 353, 5617] |
252 |
C252 |
68) |
[1165, 401, 16609] |
[1] |
1 |
[1165, 401, 16609] |
252 |
C252 |
69) |
[77, 673, 101201] |
[1] |
1 |
[77, 673, 101201] |
126 |
C126 |
70) |
[77, 673, 111673] |
[1] |
1 |
[77, 673, 111673] |
126 |
C126 |
71) |
[44, 714, 121113] |
[1] |
2 |
[44, 714, 121113] |
252 |
C2 x C126 |
72) |
[44, 654, 100593] |
[1] |
2 |
[44, 654, 100593] |
252 |
C2 x C126 |
73) |
[12, 730, 131497] |
[1] |
1 |
[12, 730, 131497] |
126 |
C126 |
74) |
[12, 806, 161977] |
[1] |
1 |
[12, 806, 161977] |
126 |
C126 |
75) |
[12, 1010, 254977] |
[1] |
1 |
[12, 1010, 254977] |
126 |
C126 |
76) |
[12, 878, 187921] |
[1] |
1 |
[12, 878, 187921] |
126 |
C126 |
77) |
[12, 962, 230929] |
[1] |
1 |
[12, 962, 230929] |
126 |
C126 |
78) |
[12, 562, 57793] |
[1] |
1 |
[12, 562, 57793] |
126 |
C126 |
79) |
[12, 902, 201049] |
[1] |
1 |
[12, 902, 201049] |
126 |
C126 |
80) |
[12, 622, 89809] |
[1] |
1 |
[12, 622, 89809] |
126 |
C126 |
81) |
[12, 938, 218233] |
[1] |
1 |
[12, 938, 218233] |
126 |
C126 |
82) |
[21, 1013, 256537] |
[1] |
1 |
[21, 1013, 256537] |
126 |
C126 |
83) |
[21, 737, 129361] |
[1] |
1 |
[21, 737, 129361] |
126 |
C126 |
84) |
[21, 694, 93193] |
[1] |
1 |
[21, 694, 93193] |
126 |
C126 |
85) |
[21, 929, 215713] |
[1] |
1 |
[21, 929, 215713] |
126 |
C126 |
86) |
[21, 782, 144481] |
[1] |
1 |
[21, 782, 144481] |
126 |
C126 |
87) |
[85, 782, 140641] |
[1] |
1 |
[85, 782, 140641] |
252 |
C252 |
88) |
[85, 726, 110009] |
[1] |
1 |
[85, 726, 110009] |
252 |
C252 |
89) |
[85, 941, 219649] |
[1] |
1 |
[85, 941, 219649] |
252 |
C2 x C126 |
90) |
[1349, 325, 9881] |
[1] |
1 |
[1349, 325, 9881] |
126 |
C126 |
91) |
[365, 529, 12929] |
[1] |
1 |
[365, 529, 12929] |
252 |
C252 |
92) |
[381, 569, 30553] |
[1] |
1 |
[381, 569, 30553] |
126 |
C126 |
93) |
[69, 629, 72673] |
[1] |
1 |
[69, 629, 72673] |
126 |
C3 x C42 |
94) |
[69, 625, 85081] |
[1] |
1 |
[69, 625, 85081] |
126 |
C126 |
95) |
[69, 601, 55369] |
[1] |
1 |
[69, 601, 55369] |
126 |
C126 |
96) |
[69, 965, 231961] |
[1] |
1 |
[69, 965, 231961] |
126 |
C126 |
97) |
[65, 606, 54369] |
[1] |
2 |
[65, 606, 54369] |
504 |
C2 x C252 |