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 240 Igusa CM invariants of non-normal (D4) fields: 164
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[661, 1182, 306977] |
[1] |
1 |
[661, 1182, 306977] |
120 |
C120 |
2) |
[165, 369, 29049] |
[1] |
1 |
[165, 369, 29049] |
240 |
C2 x C2 x C60 |
3) |
[165, 429, 45969] |
[1] |
1 |
[165, 429, 45969] |
240 |
C2 x C2 x C60 |
4) |
[437, 369, 20821] |
[1] |
1 |
[437, 369, 20821] |
120 |
C120 |
5) |
[437, 253, 7153] |
[1] |
1 |
[437, 253, 7153] |
120 |
C120 |
6) |
[60, 118, 1321] |
[2, 2] |
1 |
[60, 118, 1321] |
120 |
C2 x C2 x C30 |
7) |
[60, 342, 23241] |
[1] |
1 |
[60, 342, 23241] |
240 |
C4 x C60 |
8) |
[60, 474, 55929] |
[1] |
1 |
[60, 474, 55929] |
240 |
C4 x C60 |
9) |
[60, 282, 13881] |
[1] |
1 |
[60, 282, 13881] |
240 |
C4 x C60 |
10) |
[60, 374, 32809] |
[1] |
1 |
[60, 374, 32809] |
240 |
C4 x C60 |
11) |
[737, 279, 19276] |
[1] |
1 |
[737, 279, 19276] |
120 |
C2 x C60 |
12) |
[584, 338, 23305] |
[1] |
1 |
[584, 338, 23305] |
240 |
C4 x C60 |
13) |
[301, 321, 19665] |
[1] |
2 |
[301, 321, 19665] |
240 |
C2 x C2 x C2 x C30 |
14) |
[269, 377, 35465] |
[1] |
1 |
[269, 377, 35465] |
120 |
C2 x C60 |
15) |
[269, 453, 43165] |
[1] |
1 |
[269, 453, 43165] |
120 |
C2 x C60 |
16) |
[236, 266, 2585] |
[1] |
1 |
[236, 266, 2585] |
120 |
C2 x C60 |
17) |
[349, 361, 12949] |
[1] |
1 |
[349, 361, 12949] |
120 |
C120 |
18) |
[120, 886, 102169] |
[1] |
1 |
[120, 886, 102169] |
240 |
C2 x C2 x C2 x C30 |
19) |
[665, 606, 81169] |
[1] |
1 |
[665, 606, 81169] |
240 |
C4 x C60 |
20) |
[296, 562, 12361] |
[1] |
1 |
[296, 562, 12361] |
240 |
C2 x C2 x C60 |
21) |
[429, 293, 20497] |
[1] |
1 |
[429, 293, 20497] |
240 |
C2 x C2 x C60 |
22) |
[357, 273, 7833] |
[1] |
1 |
[357, 273, 7833] |
240 |
C2 x C2 x C60 |
23) |
[357, 309, 19497] |
[1] |
1 |
[357, 309, 19497] |
240 |
C4 x C60 |
24) |
[357, 293, 14233] |
[1] |
1 |
[357, 293, 14233] |
240 |
C2 x C2 x C60 |
25) |
[104, 298, 13777] |
[1] |
1 |
[104, 298, 13777] |
240 |
C2 x C2 x C60 |
26) |
[853, 1141, 120537] |
[1] |
1 |
[853, 1141, 120537] |
120 |
C120 |
27) |
[1544, 930, 29401] |
[1] |
1 |
[1544, 930, 29401] |
240 |
C2 x C120 |
28) |
[213, 321, 16761] |
[1] |
1 |
[213, 321, 16761] |
120 |
C2 x C60 |
29) |
[213, 238, 10753] |
[1] |
1 |
[213, 238, 10753] |
120 |
C120 |
30) |
[57, 326, 18361] |
[1] |
1 |
[57, 326, 18361] |
120 |
C2 x C60 |
31) |
[348, 266, 5161] |
[1] |
1 |
[348, 266, 5161] |
240 |
C2 x C2 x C60 |
32) |
[136, 358, 27145] |
[1] |
1 |
[136, 358, 27145] |
240 |
C4 x C60 |
33) |
[253, 361, 29481] |
[1] |
1 |
[253, 361, 29481] |
120 |
C2 x C60 |
34) |
[517, 253, 15873] |
[1] |
1 |
[517, 253, 15873] |
120 |
C2 x C2 x C30 |
35) |
[517, 241, 11289] |
[1] |
1 |
[517, 241, 11289] |
120 |
C2 x C60 |
36) |
[13, 449, 50137] |
[3, 3] |
1 |
[13, 449, 50137] |
30 |
C30 |
37) |
[13, 577, 82501] |
[1] |
1 |
[13, 577, 82501] |
120 |
C2 x C60 |
38) |
[13, 589, 86701] |
[1] |
1 |
[13, 589, 86701] |
120 |
C120 |
39) |
[13, 151, 5671] |
[1] |
1 |
[13, 151, 5671] |
120 |
C2 x C60 |
40) |
[220, 138, 3881] |
[1] |
1 |
[220, 138, 3881] |
240 |
C2 x C2 x C60 |
41) |
[8, 202, 9553] |
[3, 3] |
1 |
[8, 202, 9553] |
30 |
C30 |
42) |
[8, 110, 2225] |
[10, 10] |
1 |
[8, 110, 2225] |
12 |
C12 |
43) |
[280, 354, 28809] |
[1] |
1 |
[280, 354, 28809] |
240 |
C4 x C60 |
44) |
[5, 1238, 375161] |
[1] |
1 |
[5, 1238, 375161] |
120 |
C120 |
45) |
[5, 2006, 1005929] |
[1] |
1 |
[5, 2006, 1005929] |
120 |
C120 |
46) |
[5, 449, 50369] |
[5, 5] |
1 |
[5, 449, 50369] |
24 |
C2 x C12 |
47) |
[5, 1721, 733049] |
[1] |
1 |
[5, 1721, 733049] |
120 |
C120 |
48) |
[5, 1901, 898169] |
[1] |
1 |
[5, 1901, 898169] |
120 |
C120 |
49) |
[5, 1886, 888529] |
[1] |
1 |
[5, 1886, 888529] |
120 |
C120 |
50) |
[5, 2021, 1021049] |
[1] |
1 |
[5, 2021, 1021049] |
120 |
C120 |
51) |
[268, 346, 25641] |
[1] |
1 |
[268, 346, 25641] |
120 |
C2 x C60 |
52) |
[29, 1541, 578989] |
[1] |
1 |
[29, 1541, 578989] |
120 |
C120 |
53) |
[29, 29, 145] |
[5, 25] |
1 |
[29, 29, 145] |
6 |
C6 |
54) |
[941, 177, 7597] |
[1] |
1 |
[941, 177, 7597] |
120 |
C120 |
55) |
[124, 186, 8153] |
[1] |
1 |
[124, 186, 8153] |
120 |
C2 x C60 |
56) |
[124, 378, 31257] |
[1] |
2 |
[124, 378, 31257] |
240 |
C2 x C2 x C60 |
57) |
[440, 242, 3641] |
[1] |
1 |
[440, 242, 3641] |
240 |
C2 x C2 x C60 |
58) |
[93, 318, 23793] |
[1] |
1 |
[93, 318, 23793] |
120 |
C2 x C2 x C30 |
59) |
[93, 465, 54033] |
[1] |
1 |
[93, 465, 54033] |
120 |
C2 x C2 x C30 |
60) |
[93, 381, 32361] |
[1] |
1 |
[93, 381, 32361] |
120 |
C2 x C2 x C30 |
61) |
[589, 217, 11625] |
[5] |
1 |
[589, 217, 11625] |
24 |
C2 x C2 x C6 |
62) |
[24, 1510, 523561] |
[1] |
1 |
[24, 1510, 523561] |
120 |
C2 x C60 |
63) |
[413, 401, 31837] |
[1] |
1 |
[413, 401, 31837] |
120 |
C2 x C60 |
64) |
[285, 329, 21289] |
[1] |
1 |
[285, 329, 21289] |
240 |
C2 x C2 x C2 x C30 |
65) |
[285, 309, 15249] |
[1] |
1 |
[285, 309, 15249] |
240 |
C2 x C2 x C60 |
66) |
[428, 362, 17353] |
[1] |
1 |
[428, 362, 17353] |
120 |
C2 x C60 |
67) |
[408, 258, 6441] |
[1] |
1 |
[408, 258, 6441] |
240 |
C4 x C60 |
68) |
[40, 550, 74185] |
[1] |
1 |
[40, 550, 74185] |
240 |
C4 x C60 |
69) |
[140, 314, 15689] |
[1] |
1 |
[140, 314, 15689] |
240 |
C2 x C2 x C60 |
70) |
[509, 233, 7337] |
[1] |
1 |
[509, 233, 7337] |
120 |
C2 x C60 |
71) |
[113, 655, 105872] |
[1] |
1 |
[113, 655, 105872] |
120 |
C120 |
72) |
[521, 830, 97201] |
[1] |
1 |
[521, 830, 97201] |
120 |
C120 |
73) |
[168, 90, 513] |
[11] |
1 |
[168, 90, 513] |
24 |
C2 x C12 |
74) |
[168, 330, 18993] |
[1] |
1 |
[168, 330, 18993] |
240 |
C4 x C60 |
75) |
[89, 1355, 434776] |
[1] |
1 |
[89, 1355, 434776] |
120 |
C120 |
76) |
[565, 217, 8241] |
[1] |
1 |
[565, 217, 8241] |
240 |
C4 x C60 |
77) |
[497, 1383, 400516] |
[1] |
1 |
[497, 1383, 400516] |
120 |
C120 |
78) |
[497, 213, 5254] |
[1] |
1 |
[497, 213, 5254] |
120 |
C2 x C60 |
79) |
[1329, 967, 26116] |
[1] |
1 |
[1329, 967, 26116] |
120 |
C120 |
80) |
[53, 709, 73081] |
[1] |
1 |
[53, 709, 73081] |
120 |
C120 |
81) |
[53, 534, 70441] |
[1] |
1 |
[53, 534, 70441] |
120 |
C2 x C60 |
82) |
[341, 329, 24929] |
[1] |
1 |
[341, 329, 24929] |
120 |
C2 x C60 |
83) |
[2777, 543, 56356] |
[1] |
1 |
[2777, 543, 56356] |
360 |
C3 x C120 |
84) |
[712, 154, 5217] |
[1] |
1 |
[712, 154, 5217] |
240 |
C4 x C60 |
85) |
[37, 103, 1903] |
[1] |
1 |
[37, 103, 1903] |
120 |
C2 x C60 |
86) |
[37, 1337, 356233] |
[1] |
1 |
[37, 1337, 356233] |
120 |
C120 |
87) |
[37, 421, 34237] |
[1] |
1 |
[37, 421, 34237] |
120 |
C2 x C60 |
88) |
[536, 378, 35185] |
[1] |
1 |
[536, 378, 35185] |
120 |
C2 x C60 |
89) |
[536, 200, 5176] |
[1] |
1 |
[536, 200, 5176] |
120 |
C2 x C60 |
90) |
[293, 389, 21349] |
[1] |
1 |
[293, 389, 21349] |
120 |
C120 |
91) |
[28, 198, 9689] |
[2, 2] |
1 |
[28, 198, 9689] |
60 |
C60 |
92) |
[28, 562, 77953] |
[1] |
1 |
[28, 562, 77953] |
120 |
C2 x C60 |
93) |
[445, 285, 19305] |
[1] |
1 |
[445, 285, 19305] |
480 |
C2 x C2 x C120 |
94) |
[617, 335, 26668] |
[1] |
1 |
[617, 335, 26668] |
120 |
C2 x C60 |
95) |
[33, 318, 16833] |
[1] |
1 |
[33, 318, 16833] |
120 |
C2 x C60 |
96) |
[33, 418, 43549] |
[1] |
1 |
[33, 418, 43549] |
120 |
C2 x C2 x C30 |
97) |
[61, 126, 2993] |
[2, 2] |
1 |
[61, 126, 2993] |
40 |
C40 |
98) |
[61, 421, 42465] |
[1] |
1 |
[61, 421, 42465] |
120 |
C2 x C2 x C30 |
99) |
[61, 1177, 320697] |
[1] |
1 |
[61, 1177, 320697] |
120 |
C120 |
100) |
[593, 327, 19468] |
[1] |
1 |
[593, 327, 19468] |
120 |
C2 x C60 |
101) |
[3233, 327, 25924] |
[1] |
1 |
[3233, 327, 25924] |
240 |
C240 |
102) |
[881, 207, 10492] |
[1] |
1 |
[881, 207, 10492] |
120 |
C2 x C60 |
103) |
[17, 1731, 748984] |
[1] |
1 |
[17, 1731, 748984] |
120 |
C2 x C60 |
104) |
[17, 1902, 904129] |
[1] |
1 |
[17, 1902, 904129] |
120 |
C120 |
105) |
[17, 1931, 932152] |
[1] |
1 |
[17, 1931, 932152] |
120 |
C2 x C60 |
106) |
[17, 350, 26273] |
[1] |
1 |
[17, 350, 26273] |
120 |
C2 x C60 |
107) |
[1037, 1217, 208241] |
[1] |
1 |
[1037, 1217, 208241] |
240 |
C240 |
108) |
[264, 282, 6945] |
[1] |
1 |
[264, 282, 6945] |
240 |
C4 x C60 |
109) |
[264, 362, 30385] |
[1] |
1 |
[264, 362, 30385] |
240 |
C4 x C60 |
110) |
[173, 341, 21761] |
[1] |
1 |
[173, 341, 21761] |
120 |
C120 |
111) |
[173, 401, 38081] |
[1] |
1 |
[173, 401, 38081] |
120 |
C120 |
112) |
[545, 351, 24124] |
[1] |
1 |
[545, 351, 24124] |
240 |
C4 x C60 |
113) |
[2173, 817, 9873] |
[1] |
1 |
[2173, 817, 9873] |
240 |
C240 |
114) |
[645, 177, 3801] |
[1] |
1 |
[645, 177, 3801] |
240 |
C2 x C2 x C60 |
115) |
[773, 470, 5753] |
[1] |
1 |
[773, 470, 5753] |
120 |
C120 |
116) |
[573, 213, 7761] |
[1] |
1 |
[573, 213, 7761] |
120 |
C2 x C60 |
117) |
[232, 378, 33633] |
[1] |
2 |
[232, 378, 33633] |
480 |
C2 x C4 x C60 |
118) |
[232, 298, 10833] |
[1] |
1 |
[232, 298, 10833] |
240 |
C4 x C60 |
119) |
[232, 346, 24129] |
[1] |
1 |
[232, 346, 24129] |
240 |
C4 x C60 |
120) |
[133, 441, 48321] |
[1] |
2 |
[133, 441, 48321] |
240 |
C2 x C2 x C2 x C30 |
121) |
[776, 122, 2945] |
[1] |
1 |
[776, 122, 2945] |
240 |
C4 x C60 |
122) |
[668, 306, 20737] |
[1] |
1 |
[668, 306, 20737] |
120 |
C2 x C60 |
123) |
[77, 469, 54817] |
[1] |
1 |
[77, 469, 54817] |
120 |
C2 x C60 |
124) |
[77, 597, 88621] |
[1] |
1 |
[77, 597, 88621] |
120 |
C2 x C60 |
125) |
[701, 1613, 620825] |
[1] |
1 |
[701, 1613, 620825] |
120 |
C120 |
126) |
[701, 297, 21877] |
[1] |
1 |
[701, 297, 21877] |
120 |
C120 |
127) |
[188, 882, 103489] |
[1] |
1 |
[188, 882, 103489] |
120 |
C120 |
128) |
[653, 181, 6721] |
[1] |
1 |
[653, 181, 6721] |
120 |
C2 x C60 |
129) |
[44, 1386, 475849] |
[1] |
1 |
[44, 1386, 475849] |
120 |
C2 x C60 |
130) |
[44, 58, 137] |
[2, 14] |
1 |
[44, 58, 137] |
10 |
C10 |
131) |
[44, 1406, 454609] |
[1] |
1 |
[44, 1406, 454609] |
120 |
C120 |
132) |
[389, 193, 8437] |
[1] |
1 |
[389, 193, 8437] |
120 |
C2 x C60 |
133) |
[632, 314, 18961] |
[1] |
1 |
[632, 314, 18961] |
120 |
C120 |
134) |
[613, 205, 10353] |
[1] |
1 |
[613, 205, 10353] |
120 |
C2 x C2 x C30 |
135) |
[12, 142, 3313] |
[4, 4] |
1 |
[12, 142, 3313] |
30 |
C30 |
136) |
[12, 474, 55977] |
[1] |
1 |
[12, 474, 55977] |
120 |
C2 x C60 |
137) |
[12, 214, 11017] |
[2, 2] |
1 |
[12, 214, 11017] |
60 |
C2 x C30 |
138) |
[21, 245, 13825] |
[5, 5] |
1 |
[21, 245, 13825] |
24 |
C2 x C2 x C6 |
139) |
[21, 157, 5737] |
[3, 3] |
1 |
[21, 157, 5737] |
40 |
C40 |
140) |
[2417, 695, 71812] |
[1] |
1 |
[2417, 695, 71812] |
120 |
C120 |
141) |
[56, 178, 6521] |
[1] |
1 |
[56, 178, 6521] |
120 |
C120 |
142) |
[56, 382, 34465] |
[1] |
1 |
[56, 382, 34465] |
120 |
C2 x C60 |
143) |
[485, 401, 39109] |
[1] |
1 |
[485, 401, 39109] |
240 |
C4 x C60 |
144) |
[824, 234, 12865] |
[1] |
1 |
[824, 234, 12865] |
120 |
C2 x C60 |
145) |
[824, 98, 1577] |
[1] |
1 |
[824, 98, 1577] |
120 |
C120 |
146) |
[41, 579, 52804] |
[1] |
1 |
[41, 579, 52804] |
120 |
C120 |
147) |
[41, 1614, 650593] |
[1] |
1 |
[41, 1614, 650593] |
120 |
C120 |
148) |
[469, 277, 19065] |
[1] |
1 |
[469, 277, 19065] |
360 |
C2 x C6 x C30 |
149) |
[829, 1321, 306729] |
[1] |
1 |
[829, 1321, 306729] |
120 |
C120 |
150) |
[397, 313, 24393] |
[1] |
1 |
[397, 313, 24393] |
120 |
C2 x C60 |
151) |
[365, 289, 13489] |
[1] |
1 |
[365, 289, 13489] |
240 |
C4 x C60 |
152) |
[353, 471, 55372] |
[1] |
1 |
[353, 471, 55372] |
120 |
C2 x C60 |
153) |
[172, 706, 25537] |
[1] |
1 |
[172, 706, 25537] |
120 |
C120 |
154) |
[557, 345, 22933] |
[1] |
1 |
[557, 345, 22933] |
120 |
C2 x C60 |
155) |
[557, 233, 13433] |
[1] |
1 |
[557, 233, 13433] |
120 |
C2 x C60 |
156) |
[717, 153, 5673] |
[1] |
1 |
[717, 153, 5673] |
120 |
C2 x C60 |
157) |
[381, 317, 24265] |
[1] |
1 |
[381, 317, 24265] |
120 |
C2 x C60 |
158) |
[381, 297, 17385] |
[1] |
1 |
[381, 297, 17385] |
120 |
C2 x C2 x C30 |
159) |
[69, 217, 11617] |
[1] |
1 |
[69, 217, 11617] |
120 |
C120 |
160) |
[69, 805, 123901] |
[1] |
1 |
[69, 805, 123901] |
120 |
C2 x C60 |
161) |
[69, 366, 32385] |
[1] |
1 |
[69, 366, 32385] |
120 |
C2 x C2 x C30 |
162) |
[488, 386, 32857] |
[1] |
1 |
[488, 386, 32857] |
240 |
C4 x C60 |
163) |
[65, 1326, 388609] |
[1] |
1 |
[65, 1326, 388609] |
240 |
C4 x C60 |
164) |
[65, 591, 86524] |
[1] |
1 |
[65, 591, 86524] |
240 |
C4 x C60 |