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 216 Igusa CM invariants of non-normal (D4) fields: 57
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[157, 349, 23817] |
[1] |
1 |
[157, 349, 23817] |
108 |
C2 x C54 |
2) |
[301, 349, 28569] |
[1] |
1 |
[301, 349, 28569] |
108 |
C6 x C18 |
3) |
[629, 197, 9545] |
[1] |
1 |
[629, 197, 9545] |
216 |
C2 x C108 |
4) |
[349, 313, 20217] |
[1] |
1 |
[349, 313, 20217] |
108 |
C2 x C54 |
5) |
[461, 241, 5185] |
[1] |
1 |
[461, 241, 5185] |
108 |
C6 x C18 |
6) |
[461, 257, 10865] |
[1] |
1 |
[461, 257, 10865] |
108 |
C2 x C54 |
7) |
[797, 113, 2993] |
[1] |
1 |
[797, 113, 2993] |
108 |
C108 |
8) |
[13, 33, 113] |
[7, 63] |
1 |
[13, 33, 113] |
3 |
C3 |
9) |
[13, 942, 196673] |
[1] |
1 |
[13, 942, 196673] |
108 |
C6 x C18 |
10) |
[13, 2438, 810169] |
[1] |
1 |
[13, 2438, 810169] |
108 |
C108 |
11) |
[13, 918, 110009] |
[1] |
1 |
[13, 918, 110009] |
108 |
C108 |
12) |
[13, 382, 28993] |
[1] |
1 |
[13, 382, 28993] |
108 |
C108 |
13) |
[13, 406, 41001] |
[2, 2] |
1 |
[13, 406, 41001] |
36 |
C2 x C18 |
14) |
[13, 2222, 627793] |
[1] |
1 |
[13, 2222, 627793] |
108 |
C3 x C36 |
15) |
[8, 762, 143809] |
[1] |
1 |
[8, 762, 143809] |
108 |
C108 |
16) |
[8, 890, 175553] |
[1] |
1 |
[8, 890, 175553] |
108 |
C2 x C54 |
17) |
[8, 1146, 211201] |
[1] |
1 |
[8, 1146, 211201] |
108 |
C3 x C36 |
18) |
[8, 1002, 223153] |
[1] |
1 |
[8, 1002, 223153] |
108 |
C2 x C54 |
19) |
[8, 1434, 290977] |
[1] |
1 |
[8, 1434, 290977] |
108 |
C2 x C54 |
20) |
[5, 2521, 1494329] |
[1] |
1 |
[5, 2521, 1494329] |
108 |
C108 |
21) |
[5, 1077, 232201] |
[1] |
1 |
[5, 1077, 232201] |
108 |
C108 |
22) |
[5, 389, 37769] |
[7, 7] |
1 |
[5, 389, 37769] |
18 |
C18 |
23) |
[5, 2221, 1001009] |
[1] |
1 |
[5, 2221, 1001009] |
108 |
C108 |
24) |
[5, 1573, 612281] |
[1] |
1 |
[5, 1573, 612281] |
108 |
C3 x C36 |
25) |
[5, 1801, 789449] |
[1] |
1 |
[5, 1801, 789449] |
108 |
C108 |
26) |
[5, 2581, 1661609] |
[1] |
1 |
[5, 2581, 1661609] |
108 |
C108 |
27) |
[5, 2201, 1080689] |
[1] |
1 |
[5, 2201, 1080689] |
108 |
C108 |
28) |
[5, 1966, 873809] |
[1] |
1 |
[5, 1966, 873809] |
108 |
C108 |
29) |
[5, 1257, 333961] |
[1] |
1 |
[5, 1257, 333961] |
108 |
C108 |
30) |
[5, 150, 4905] |
[6, 6] |
1 |
[5, 150, 4905] |
12 |
C2 x C6 |
31) |
[5, 2326, 1183289] |
[1] |
1 |
[5, 2326, 1183289] |
108 |
C108 |
32) |
[5, 489, 59769] |
[3, 3] |
1 |
[5, 489, 59769] |
36 |
C2 x C18 |
33) |
[5, 2161, 962449] |
[1] |
1 |
[5, 2161, 962449] |
108 |
C108 |
34) |
[5, 1849, 849089] |
[1] |
1 |
[5, 1849, 849089] |
108 |
C108 |
35) |
[5, 1369, 456289] |
[1] |
1 |
[5, 1369, 456289] |
108 |
C2 x C54 |
36) |
[29, 446, 49265] |
[1] |
1 |
[29, 446, 49265] |
108 |
C2 x C54 |
37) |
[93, 405, 38193] |
[1] |
1 |
[93, 405, 38193] |
108 |
C2 x C54 |
38) |
[757, 133, 4233] |
[1] |
1 |
[757, 133, 4233] |
108 |
C2 x C54 |
39) |
[152, 338, 21113] |
[1] |
1 |
[152, 338, 21113] |
108 |
C108 |
40) |
[509, 381, 33109] |
[1] |
1 |
[509, 381, 33109] |
108 |
C108 |
41) |
[89, 262, 4345] |
[1] |
1 |
[89, 262, 4345] |
108 |
C2 x C54 |
42) |
[53, 485, 58793] |
[1] |
1 |
[53, 485, 58793] |
108 |
C2 x C54 |
43) |
[53, 461, 52481] |
[1] |
1 |
[53, 461, 52481] |
108 |
C2 x C54 |
44) |
[53, 425, 43553] |
[1] |
1 |
[53, 425, 43553] |
108 |
C108 |
45) |
[293, 281, 7361] |
[1] |
1 |
[293, 281, 7361] |
108 |
C108 |
46) |
[33, 374, 30217] |
[1] |
1 |
[33, 374, 30217] |
108 |
C2 x C54 |
47) |
[61, 33, 257] |
[15] |
1 |
[61, 33, 257] |
9 |
C9 |
48) |
[677, 169, 5617] |
[1] |
1 |
[677, 169, 5617] |
108 |
C108 |
49) |
[173, 477, 49573] |
[1] |
1 |
[173, 477, 49573] |
108 |
C108 |
50) |
[773, 125, 3713] |
[1] |
1 |
[773, 125, 3713] |
108 |
C108 |
51) |
[524, 218, 3497] |
[1] |
1 |
[524, 218, 3497] |
108 |
C108 |
52) |
[12, 1202, 343873] |
[1] |
1 |
[12, 1202, 343873] |
108 |
C2 x C54 |
53) |
[12, 550, 50233] |
[1] |
1 |
[12, 550, 50233] |
108 |
C2 x C54 |
54) |
[469, 253, 10257] |
[1] |
1 |
[469, 253, 10257] |
324 |
C6 x C54 |
55) |
[397, 289, 16017] |
[1] |
1 |
[397, 289, 16017] |
108 |
C2 x C54 |
56) |
[472, 274, 18297] |
[1] |
1 |
[472, 274, 18297] |
108 |
C108 |
57) |
[69, 197, 8305] |
[3, 3] |
1 |
[69, 197, 8305] |
36 |
C2 x C18 |