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 392 Igusa CM invariants of non-normal (D4) fields: 79
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[165, 677, 92761] |
[1] |
1 |
[165, 677, 92761] |
392 |
C2 x C196 |
2) |
[165, 686, 115009] |
[1] |
1 |
[165, 686, 115009] |
392 |
C2 x C196 |
3) |
[237, 725, 110017] |
[1] |
1 |
[237, 725, 110017] |
196 |
C196 |
4) |
[237, 541, 29977] |
[1] |
1 |
[237, 541, 29977] |
196 |
C196 |
5) |
[60, 526, 60529] |
[1] |
1 |
[60, 526, 60529] |
392 |
C2 x C196 |
6) |
[229, 905, 204241] |
[1] |
1 |
[229, 905, 204241] |
588 |
C588 |
7) |
[376, 270, 16721] |
[1] |
1 |
[376, 270, 16721] |
196 |
C2 x C98 |
8) |
[88, 830, 169057] |
[1] |
1 |
[88, 830, 169057] |
196 |
C2 x C98 |
9) |
[988, 458, 16873] |
[1] |
1 |
[988, 458, 16873] |
392 |
C2 x C196 |
10) |
[296, 382, 6881] |
[1] |
1 |
[296, 382, 6881] |
392 |
C2 x C2 x C98 |
11) |
[296, 430, 45041] |
[1] |
1 |
[296, 430, 45041] |
392 |
C2 x C2 x C98 |
12) |
[129, 566, 28489] |
[1] |
1 |
[129, 566, 28489] |
196 |
C196 |
13) |
[213, 566, 66457] |
[1] |
1 |
[213, 566, 66457] |
196 |
C196 |
14) |
[109, 734, 118993] |
[1] |
1 |
[109, 734, 118993] |
196 |
C2 x C98 |
15) |
[109, 489, 33593] |
[1] |
1 |
[109, 489, 33593] |
196 |
C196 |
16) |
[733, 513, 12833] |
[1] |
1 |
[733, 513, 12833] |
588 |
C588 |
17) |
[205, 609, 60689] |
[1] |
1 |
[205, 609, 60689] |
392 |
C2 x C196 |
18) |
[309, 725, 109081] |
[1] |
1 |
[309, 725, 109081] |
196 |
C196 |
19) |
[309, 785, 141001] |
[1] |
1 |
[309, 785, 141001] |
196 |
C196 |
20) |
[309, 557, 29281] |
[1] |
1 |
[309, 557, 29281] |
196 |
C14 x C14 |
21) |
[1077, 425, 12577] |
[1] |
1 |
[1077, 425, 12577] |
196 |
C7 x C28 |
22) |
[1336, 338, 16537] |
[1] |
1 |
[1336, 338, 16537] |
196 |
C2 x C98 |
23) |
[13, 745, 125857] |
[1] |
1 |
[13, 745, 125857] |
196 |
C196 |
24) |
[76, 914, 206113] |
[1] |
1 |
[76, 914, 206113] |
196 |
C2 x C98 |
25) |
[76, 630, 62441] |
[1] |
1 |
[76, 630, 62441] |
196 |
C2 x C98 |
26) |
[8, 986, 242977] |
[1] |
1 |
[8, 986, 242977] |
196 |
C2 x C98 |
27) |
[93, 613, 76993] |
[1] |
1 |
[93, 613, 76993] |
196 |
C2 x C98 |
28) |
[93, 977, 238609] |
[1] |
1 |
[93, 977, 238609] |
196 |
C2 x C98 |
29) |
[93, 953, 225913] |
[1] |
1 |
[93, 953, 225913] |
196 |
C2 x C98 |
30) |
[93, 830, 170737] |
[1] |
1 |
[93, 830, 170737] |
196 |
C196 |
31) |
[93, 433, 21553] |
[1] |
1 |
[93, 433, 21553] |
196 |
C196 |
32) |
[1357, 341, 26017] |
[1] |
1 |
[1357, 341, 26017] |
196 |
C196 |
33) |
[24, 562, 30361] |
[1] |
1 |
[24, 562, 30361] |
196 |
C2 x C98 |
34) |
[24, 574, 74593] |
[1] |
1 |
[24, 574, 74593] |
196 |
C2 x C98 |
35) |
[285, 701, 97129] |
[1] |
1 |
[285, 701, 97129] |
392 |
C2 x C196 |
36) |
[105, 526, 8689] |
[1] |
1 |
[105, 526, 8689] |
392 |
C2 x C2 x C98 |
37) |
[105, 182, 6601] |
[1] |
1 |
[105, 182, 6601] |
392 |
C2 x C196 |
38) |
[141, 377, 27601] |
[1] |
1 |
[141, 377, 27601] |
196 |
C196 |
39) |
[141, 893, 195097] |
[1] |
1 |
[141, 893, 195097] |
196 |
C2 x C98 |
40) |
[40, 666, 104129] |
[1] |
1 |
[40, 666, 104129] |
392 |
C2 x C2 x C98 |
41) |
[140, 362, 12601] |
[1] |
1 |
[140, 362, 12601] |
392 |
C2 x C2 x C98 |
42) |
[168, 526, 14737] |
[1] |
1 |
[168, 526, 14737] |
392 |
C2 x C2 x C98 |
43) |
[156, 314, 19033] |
[1] |
1 |
[156, 314, 19033] |
392 |
C2 x C196 |
44) |
[156, 554, 46153] |
[1] |
1 |
[156, 554, 46153] |
392 |
C2 x C2 x C98 |
45) |
[53, 937, 217889] |
[1] |
1 |
[53, 937, 217889] |
196 |
C2 x C98 |
46) |
[1189, 425, 42481] |
[1] |
1 |
[1189, 425, 42481] |
392 |
C2 x C2 x C98 |
47) |
[341, 589, 41633] |
[1] |
1 |
[341, 589, 41633] |
196 |
C2 x C98 |
48) |
[184, 638, 95137] |
[1] |
1 |
[184, 638, 95137] |
196 |
C2 x C98 |
49) |
[184, 770, 133321] |
[1] |
1 |
[184, 770, 133321] |
196 |
C196 |
50) |
[184, 482, 16681] |
[1] |
1 |
[184, 482, 16681] |
196 |
C14 x C14 |
51) |
[37, 678, 100121] |
[1] |
1 |
[37, 678, 100121] |
196 |
C196 |
52) |
[28, 798, 158753] |
[1] |
1 |
[28, 798, 158753] |
196 |
C2 x C98 |
53) |
[28, 642, 91841] |
[1] |
1 |
[28, 642, 91841] |
196 |
C196 |
54) |
[28, 666, 108089] |
[1] |
1 |
[28, 666, 108089] |
196 |
C196 |
55) |
[316, 578, 38017] |
[1] |
1 |
[316, 578, 38017] |
588 |
C14 x C42 |
56) |
[501, 761, 141649] |
[1] |
1 |
[501, 761, 141649] |
196 |
C7 x C28 |
57) |
[204, 566, 59689] |
[1] |
1 |
[204, 566, 59689] |
392 |
C2 x C196 |
58) |
[33, 422, 39769] |
[1] |
1 |
[33, 422, 39769] |
196 |
C196 |
59) |
[1757, 145, 4817] |
[1] |
1 |
[1757, 145, 4817] |
196 |
C196 |
60) |
[677, 541, 24257] |
[1] |
1 |
[677, 541, 24257] |
196 |
C196 |
61) |
[173, 670, 109457] |
[1] |
1 |
[173, 670, 109457] |
196 |
C196 |
62) |
[77, 565, 63617] |
[1] |
1 |
[77, 565, 63617] |
196 |
C196 |
63) |
[77, 742, 117929] |
[1] |
1 |
[77, 742, 117929] |
196 |
C2 x C98 |
64) |
[389, 517, 6041] |
[1] |
1 |
[389, 517, 6041] |
196 |
C196 |
65) |
[613, 301, 10237] |
[1] |
1 |
[613, 301, 10237] |
196 |
C196 |
66) |
[12, 682, 100729] |
[1] |
1 |
[12, 682, 100729] |
196 |
C2 x C98 |
67) |
[1293, 353, 15313] |
[1] |
1 |
[1293, 353, 15313] |
196 |
C196 |
68) |
[85, 977, 238441] |
[1] |
1 |
[85, 977, 238441] |
392 |
C2 x C196 |
69) |
[616, 554, 26833] |
[1] |
1 |
[616, 554, 26833] |
392 |
C2 x C196 |
70) |
[73, 422, 34009] |
[1] |
1 |
[73, 422, 34009] |
196 |
C196 |
71) |
[1517, 253, 6521] |
[1] |
1 |
[1517, 253, 6521] |
392 |
C14 x C28 |
72) |
[1580, 226, 6449] |
[1] |
1 |
[1580, 226, 6449] |
392 |
C2 x C2 x C98 |
73) |
[469, 569, 29233] |
[1] |
1 |
[469, 569, 29233] |
588 |
C2 x C294 |
74) |
[424, 174, 5873] |
[1] |
1 |
[424, 174, 5873] |
392 |
C2 x C2 x C98 |
75) |
[101, 961, 230249] |
[1] |
1 |
[101, 961, 230249] |
196 |
C196 |
76) |
[1324, 330, 6041] |
[1] |
1 |
[1324, 330, 6041] |
196 |
C2 x C98 |
77) |
[69, 598, 49657] |
[1] |
1 |
[69, 598, 49657] |
196 |
C2 x C98 |
78) |
[69, 758, 125977] |
[1] |
1 |
[69, 758, 125977] |
196 |
C2 x C98 |
79) |
[69, 454, 41593] |
[1] |
1 |
[69, 454, 41593] |
196 |
C196 |