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 28 Igusa CM invariants of non-normal (D4) fields: 140
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[157, 510, 2225] |
[1] |
2 |
[157, 510, 2225] |
28 |
C28 |
2) |
[237, 233, 241] |
[1] |
1 |
[237, 233, 241] |
14 |
C14 |
3) |
[437, 65, 73] |
[1] |
1 |
[437, 65, 73] |
14 |
C14 |
4) |
[437, 90, 277] |
[1] |
1 |
[437, 90, 277] |
14 |
C14 |
5) |
[236, 40, 164] |
[1] |
1 |
[236, 40, 164] |
14 |
C14 |
6) |
[88, 78, 113] |
[1] |
1 |
[88, 78, 113] |
14 |
C14 |
7) |
[213, 65, 577] |
[1] |
1 |
[213, 65, 577] |
14 |
C14 |
8) |
[213, 345, 6273] |
[1] |
1 |
[213, 345, 6273] |
14 |
C14 |
9) |
[205, 166, 3609] |
[1] |
1 |
[205, 166, 3609] |
28 |
C28 |
10) |
[821, 262, 4025] |
[1] |
1 |
[821, 262, 4025] |
14 |
C14 |
11) |
[13, 590, 40225] |
[1] |
2 |
[13, 590, 40225] |
28 |
C28 |
12) |
[13, 294, 11417] |
[1] |
2 |
[13, 294, 11417] |
28 |
C28 |
13) |
[13, 233, 10033] |
[1] |
1 |
[13, 233, 10033] |
14 |
C14 |
14) |
[13, 473, 52393] |
[1] |
2 |
[13, 473, 52393] |
28 |
C28 |
15) |
[13, 485, 52225] |
[1] |
2 |
[13, 485, 52225] |
28 |
C28 |
16) |
[13, 350, 13777] |
[1] |
1 |
[13, 350, 13777] |
14 |
C14 |
17) |
[13, 257, 11569] |
[1] |
1 |
[13, 257, 11569] |
14 |
C14 |
18) |
[13, 174, 2369] |
[1] |
1 |
[13, 174, 2369] |
14 |
C14 |
19) |
[8, 158, 4193] |
[1] |
1 |
[8, 158, 4193] |
14 |
C14 |
20) |
[8, 56, 622] |
[1] |
1 |
[8, 56, 622] |
14 |
C14 |
21) |
[8, 114, 3217] |
[1] |
1 |
[8, 114, 3217] |
28 |
C28 |
22) |
[8, 222, 11169] |
[1] |
2 |
[8, 222, 11169] |
28 |
C2 x C14 |
23) |
[8, 330, 15057] |
[1] |
2 |
[8, 330, 15057] |
28 |
C2 x C14 |
24) |
[8, 262, 17089] |
[1] |
1 |
[8, 262, 17089] |
28 |
C2 x C14 |
25) |
[8, 142, 4393] |
[1] |
1 |
[8, 142, 4393] |
28 |
C2 x C14 |
26) |
[8, 338, 14449] |
[1] |
1 |
[8, 338, 14449] |
28 |
C28 |
27) |
[8, 122, 2369] |
[1] |
1 |
[8, 122, 2369] |
14 |
C14 |
28) |
[8, 238, 12593] |
[1] |
2 |
[8, 238, 12593] |
28 |
C2 x C14 |
29) |
[8, 234, 13561] |
[1] |
1 |
[8, 234, 13561] |
28 |
C2 x C14 |
30) |
[8, 510, 36225] |
[1] |
4 |
[8, 510, 36225] |
56 |
C2 x C2 x C14 |
31) |
[8, 48, 334] |
[1] |
1 |
[8, 48, 334] |
14 |
C14 |
32) |
[8, 710, 97225] |
[1] |
1 |
[8, 710, 97225] |
28 |
C28 |
33) |
[8, 770, 103225] |
[1] |
2 |
[8, 770, 103225] |
28 |
C28 |
34) |
[8, 72, 1198] |
[1] |
1 |
[8, 72, 1198] |
14 |
C14 |
35) |
[8, 170, 7217] |
[1] |
1 |
[8, 170, 7217] |
14 |
C14 |
36) |
[8, 162, 3361] |
[1] |
2 |
[8, 162, 3361] |
28 |
C28 |
37) |
[8, 94, 2177] |
[1] |
1 |
[8, 94, 2177] |
14 |
C14 |
38) |
[8, 106, 1457] |
[1] |
1 |
[8, 106, 1457] |
14 |
C14 |
39) |
[8, 122, 1921] |
[1] |
1 |
[8, 122, 1921] |
14 |
C14 |
40) |
[8, 342, 25369] |
[1] |
1 |
[8, 342, 25369] |
14 |
C14 |
41) |
[8, 502, 39673] |
[1] |
1 |
[8, 502, 39673] |
14 |
C14 |
42) |
[8, 450, 28153] |
[1] |
1 |
[8, 450, 28153] |
14 |
C14 |
43) |
[8, 120, 2350] |
[1] |
2 |
[8, 120, 2350] |
28 |
C2 x C14 |
44) |
[1957, 45, 17] |
[1] |
1 |
[1957, 45, 17] |
42 |
C42 |
45) |
[5, 381, 34189] |
[1] |
1 |
[5, 381, 34189] |
14 |
C14 |
46) |
[5, 501, 53289] |
[1] |
2 |
[5, 501, 53289] |
28 |
C2 x C14 |
47) |
[5, 202, 10021] |
[1] |
1 |
[5, 202, 10021] |
14 |
C14 |
48) |
[5, 401, 36949] |
[1] |
1 |
[5, 401, 36949] |
14 |
C14 |
49) |
[5, 366, 27009] |
[1] |
2 |
[5, 366, 27009] |
28 |
C28 |
50) |
[5, 246, 13849] |
[1] |
1 |
[5, 246, 13849] |
14 |
C14 |
51) |
[5, 154, 5209] |
[1] |
2 |
[5, 154, 5209] |
28 |
C28 |
52) |
[5, 333, 27441] |
[1] |
2 |
[5, 333, 27441] |
28 |
C28 |
53) |
[5, 549, 61569] |
[1] |
2 |
[5, 549, 61569] |
28 |
C28 |
54) |
[5, 156, 5764] |
[1] |
1 |
[5, 156, 5764] |
28 |
C2 x C14 |
55) |
[5, 681, 103689] |
[1] |
2 |
[5, 681, 103689] |
28 |
C2 x C14 |
56) |
[5, 861, 180369] |
[1] |
4 |
[5, 861, 180369] |
56 |
C2 x C28 |
57) |
[5, 277, 17821] |
[1] |
1 |
[5, 277, 17821] |
14 |
C14 |
58) |
[5, 166, 6169] |
[1] |
1 |
[5, 166, 6169] |
14 |
C14 |
59) |
[5, 741, 131989] |
[1] |
2 |
[5, 741, 131989] |
28 |
C2 x C14 |
60) |
[5, 108, 2596] |
[1] |
2 |
[5, 108, 2596] |
28 |
C2 x C14 |
61) |
[5, 301, 22289] |
[1] |
1 |
[5, 301, 22289] |
14 |
C14 |
62) |
[5, 721, 107849] |
[1] |
2 |
[5, 721, 107849] |
28 |
C2 x C14 |
63) |
[5, 246, 14809] |
[1] |
1 |
[5, 246, 14809] |
14 |
C14 |
64) |
[5, 481, 47029] |
[1] |
1 |
[5, 481, 47029] |
14 |
C14 |
65) |
[5, 289, 18569] |
[1] |
1 |
[5, 289, 18569] |
14 |
C14 |
66) |
[5, 137, 4681] |
[1] |
1 |
[5, 137, 4681] |
14 |
C14 |
67) |
[5, 297, 18801] |
[1] |
2 |
[5, 297, 18801] |
28 |
C28 |
68) |
[5, 298, 20581] |
[1] |
1 |
[5, 298, 20581] |
14 |
C14 |
69) |
[5, 309, 23089] |
[1] |
1 |
[5, 309, 23089] |
14 |
C14 |
70) |
[5, 114, 3169] |
[1] |
1 |
[5, 114, 3169] |
28 |
C28 |
71) |
[5, 249, 13969] |
[1] |
1 |
[5, 249, 13969] |
14 |
C14 |
72) |
[5, 274, 17149] |
[1] |
1 |
[5, 274, 17149] |
14 |
C14 |
73) |
[5, 189, 7729] |
[1] |
1 |
[5, 189, 7729] |
14 |
C14 |
74) |
[5, 861, 167629] |
[1] |
2 |
[5, 861, 167629] |
28 |
C2 x C14 |
75) |
[5, 111, 3049] |
[1] |
1 |
[5, 111, 3049] |
28 |
C28 |
76) |
[5, 269, 15089] |
[1] |
1 |
[5, 269, 15089] |
14 |
C14 |
77) |
[29, 78, 1057] |
[1] |
1 |
[29, 78, 1057] |
14 |
C14 |
78) |
[29, 301, 13769] |
[1] |
2 |
[29, 301, 13769] |
28 |
C2 x C14 |
79) |
[29, 550, 19481] |
[1] |
2 |
[29, 550, 19481] |
28 |
C2 x C14 |
80) |
[29, 105, 2169] |
[1] |
2 |
[29, 105, 2169] |
28 |
C28 |
81) |
[29, 289, 3473] |
[1] |
1 |
[29, 289, 3473] |
14 |
C14 |
82) |
[29, 249, 4473] |
[1] |
2 |
[29, 249, 4473] |
28 |
C2 x C14 |
83) |
[1256, 142, 17] |
[1] |
1 |
[1256, 142, 17] |
28 |
C2 x C14 |
84) |
[93, 365, 4825] |
[1] |
2 |
[93, 365, 4825] |
28 |
C2 x C14 |
85) |
[24, 76, 1348] |
[1] |
1 |
[24, 76, 1348] |
14 |
C14 |
86) |
[1781, 129, 153] |
[1] |
2 |
[1781, 129, 153] |
56 |
C2 x C2 x C14 |
87) |
[141, 69, 873] |
[1] |
1 |
[141, 69, 873] |
14 |
C14 |
88) |
[152, 62, 353] |
[1] |
1 |
[152, 62, 353] |
14 |
C14 |
89) |
[152, 116, 932] |
[1] |
1 |
[152, 116, 932] |
14 |
C14 |
90) |
[40, 254, 3169] |
[1] |
1 |
[40, 254, 3169] |
28 |
C2 x C14 |
91) |
[149, 102, 217] |
[1] |
1 |
[149, 102, 217] |
14 |
C14 |
92) |
[149, 65, 721] |
[1] |
1 |
[149, 65, 721] |
14 |
C14 |
93) |
[53, 190, 1393] |
[1] |
1 |
[53, 190, 1393] |
14 |
C14 |
94) |
[53, 205, 2225] |
[1] |
2 |
[53, 205, 2225] |
28 |
C28 |
95) |
[53, 366, 2961] |
[1] |
2 |
[53, 366, 2961] |
28 |
C2 x C14 |
96) |
[53, 385, 20825] |
[1] |
4 |
[53, 385, 20825] |
56 |
C2 x C2 x C14 |
97) |
[1052, 208, 1348] |
[1] |
1 |
[1052, 208, 1348] |
14 |
C14 |
98) |
[37, 545, 22225] |
[1] |
2 |
[37, 545, 22225] |
28 |
C2 x C14 |
99) |
[37, 326, 5257] |
[1] |
1 |
[37, 326, 5257] |
14 |
C14 |
100) |
[293, 414, 657] |
[1] |
2 |
[293, 414, 657] |
28 |
C28 |
101) |
[28, 64, 772] |
[1] |
1 |
[28, 64, 772] |
14 |
C14 |
102) |
[445, 581, 35329] |
[1] |
1 |
[445, 581, 35329] |
56 |
C56 |
103) |
[33, 43, 388] |
[1] |
1 |
[33, 43, 388] |
14 |
C14 |
104) |
[197, 342, 873] |
[1] |
2 |
[197, 342, 873] |
28 |
C28 |
105) |
[1461, 293, 21097] |
[1] |
1 |
[1461, 293, 21097] |
14 |
C14 |
106) |
[1304, 294, 16393] |
[1] |
1 |
[1304, 294, 16393] |
42 |
C42 |
107) |
[232, 196, 8676] |
[1] |
1 |
[232, 196, 8676] |
28 |
C2 x C14 |
108) |
[133, 153, 233] |
[1] |
1 |
[133, 153, 233] |
14 |
C14 |
109) |
[77, 281, 1241] |
[1] |
1 |
[77, 281, 1241] |
14 |
C14 |
110) |
[77, 61, 449] |
[1] |
1 |
[77, 61, 449] |
14 |
C14 |
111) |
[77, 69, 1017] |
[1] |
2 |
[77, 69, 1017] |
28 |
C2 x C14 |
112) |
[653, 393, 30613] |
[1] |
1 |
[653, 393, 30613] |
14 |
C14 |
113) |
[44, 72, 1252] |
[1] |
1 |
[44, 72, 1252] |
14 |
C14 |
114) |
[44, 120, 3204] |
[1] |
2 |
[44, 120, 3204] |
28 |
C2 x C14 |
115) |
[12, 142, 4609] |
[1] |
1 |
[12, 142, 4609] |
14 |
C14 |
116) |
[12, 122, 1993] |
[1] |
1 |
[12, 122, 1993] |
14 |
C14 |
117) |
[12, 70, 550] |
[1] |
2 |
[12, 70, 550] |
28 |
C2 x C14 |
118) |
[12, 350, 11425] |
[1] |
2 |
[12, 350, 11425] |
28 |
C2 x C14 |
119) |
[12, 218, 4969] |
[1] |
1 |
[12, 218, 4969] |
14 |
C14 |
120) |
[12, 178, 5893] |
[1] |
2 |
[12, 178, 5893] |
28 |
C2 x C14 |
121) |
[12, 34, 214] |
[1] |
1 |
[12, 34, 214] |
14 |
C14 |
122) |
[12, 100, 1177] |
[1] |
2 |
[12, 100, 1177] |
28 |
C2 x C14 |
123) |
[12, 158, 4513] |
[1] |
1 |
[12, 158, 4513] |
14 |
C14 |
124) |
[12, 214, 3949] |
[1] |
2 |
[12, 214, 3949] |
28 |
C2 x C14 |
125) |
[12, 178, 6193] |
[1] |
1 |
[12, 178, 6193] |
14 |
C14 |
126) |
[12, 76, 1417] |
[1] |
2 |
[12, 76, 1417] |
28 |
C2 x C14 |
127) |
[12, 58, 649] |
[1] |
1 |
[12, 58, 649] |
14 |
C14 |
128) |
[12, 112, 949] |
[1] |
2 |
[12, 112, 949] |
28 |
C2 x C14 |
129) |
[21, 85, 1549] |
[1] |
1 |
[21, 85, 1549] |
14 |
C14 |
130) |
[21, 85, 1801] |
[1] |
1 |
[21, 85, 1801] |
14 |
C14 |
131) |
[21, 281, 4993] |
[1] |
1 |
[21, 281, 4993] |
14 |
C14 |
132) |
[21, 61, 673] |
[1] |
1 |
[21, 61, 673] |
14 |
C14 |
133) |
[21, 125, 1129] |
[1] |
1 |
[21, 125, 1129] |
14 |
C14 |
134) |
[21, 73, 697] |
[1] |
1 |
[21, 73, 697] |
14 |
C14 |
135) |
[85, 221, 11169] |
[1] |
1 |
[85, 221, 11169] |
28 |
C28 |
136) |
[85, 289, 17289] |
[1] |
1 |
[85, 289, 17289] |
28 |
C28 |
137) |
[56, 876, 51844] |
[1] |
1 |
[56, 876, 51844] |
14 |
C14 |
138) |
[485, 209, 7889] |
[1] |
1 |
[485, 209, 7889] |
28 |
C28 |
139) |
[353, 311, 4324] |
[1] |
1 |
[353, 311, 4324] |
14 |
C14 |
140) |
[101, 361, 1649] |
[1] |
1 |
[101, 361, 1649] |
14 |
C14 |