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 100 Igusa CM invariants of non-normal (D4) fields: 180
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[1893, 853, 45133] |
[1] |
1 |
[1893, 853, 45133] |
50 |
C50 |
2) |
[2429, 645, 1381] |
[1] |
1 |
[2429, 645, 1381] |
150 |
C150 |
3) |
[1529, 959, 61348] |
[1] |
2 |
[1529, 959, 61348] |
100 |
C2 x C50 |
4) |
[237, 137, 4633] |
[1] |
1 |
[237, 137, 4633] |
50 |
C50 |
5) |
[60, 664, 72724] |
[1] |
2 |
[60, 664, 72724] |
200 |
C2 x C100 |
6) |
[60, 214, 10909] |
[1] |
2 |
[60, 214, 10909] |
200 |
C2 x C100 |
7) |
[584, 930, 5401] |
[1] |
1 |
[584, 930, 5401] |
100 |
C100 |
8) |
[409, 355, 1956] |
[1] |
1 |
[409, 355, 1956] |
50 |
C50 |
9) |
[236, 754, 6193] |
[1] |
1 |
[236, 754, 6193] |
50 |
C50 |
10) |
[376, 244, 1348] |
[1] |
2 |
[376, 244, 1348] |
100 |
C2 x C50 |
11) |
[3737, 75, 472] |
[1] |
1 |
[3737, 75, 472] |
100 |
C100 |
12) |
[88, 292, 18148] |
[1] |
2 |
[88, 292, 18148] |
100 |
C2 x C50 |
13) |
[1937, 966, 231352] |
[1] |
1 |
[1937, 966, 231352] |
300 |
C300 |
14) |
[104, 186, 7713] |
[1] |
2 |
[104, 186, 7713] |
200 |
C2 x C10 x C10 |
15) |
[104, 228, 2596] |
[1] |
1 |
[104, 228, 2596] |
100 |
C100 |
16) |
[161, 1135, 260836] |
[1] |
1 |
[161, 1135, 260836] |
50 |
C50 |
17) |
[161, 162, 5917] |
[1] |
1 |
[161, 162, 5917] |
50 |
C50 |
18) |
[109, 177, 6497] |
[1] |
1 |
[109, 177, 6497] |
50 |
C50 |
19) |
[97, 595, 25432] |
[1] |
2 |
[97, 595, 25432] |
100 |
C2 x C50 |
20) |
[57, 1231, 359332] |
[1] |
1 |
[57, 1231, 359332] |
50 |
C50 |
21) |
[348, 70, 877] |
[1] |
2 |
[348, 70, 877] |
200 |
C10 x C20 |
22) |
[205, 129, 1649] |
[1] |
1 |
[205, 129, 1649] |
100 |
C100 |
23) |
[253, 129, 4097] |
[1] |
1 |
[253, 129, 4097] |
50 |
C50 |
24) |
[377, 237, 2638] |
[1] |
1 |
[377, 237, 2638] |
100 |
C100 |
25) |
[217, 823, 28228] |
[1] |
1 |
[217, 823, 28228] |
50 |
C5 x C10 |
26) |
[13, 438, 27161] |
[1] |
1 |
[13, 438, 27161] |
50 |
C50 |
27) |
[76, 102, 2297] |
[1] |
1 |
[76, 102, 2297] |
50 |
C50 |
28) |
[76, 34, 118] |
[1] |
1 |
[76, 34, 118] |
50 |
C50 |
29) |
[8, 906, 204409] |
[1] |
2 |
[8, 906, 204409] |
100 |
C2 x C50 |
30) |
[8, 666, 98089] |
[1] |
2 |
[8, 666, 98089] |
100 |
C2 x C50 |
31) |
[8, 994, 202009] |
[1] |
1 |
[8, 994, 202009] |
50 |
C50 |
32) |
[8, 1266, 399337] |
[1] |
1 |
[8, 1266, 399337] |
50 |
C50 |
33) |
[8, 1362, 416329] |
[1] |
1 |
[8, 1362, 416329] |
50 |
C50 |
34) |
[8, 1110, 160057] |
[1] |
1 |
[8, 1110, 160057] |
50 |
C50 |
35) |
[8, 934, 218017] |
[1] |
2 |
[8, 934, 218017] |
100 |
C2 x C50 |
36) |
[8, 1830, 834025] |
[1] |
2 |
[8, 1830, 834025] |
100 |
C2 x C50 |
37) |
[8, 870, 188833] |
[1] |
2 |
[8, 870, 188833] |
100 |
C5 x C20 |
38) |
[8, 442, 48553] |
[1] |
2 |
[8, 442, 48553] |
100 |
C2 x C50 |
39) |
[8, 1106, 196297] |
[1] |
1 |
[8, 1106, 196297] |
50 |
C50 |
40) |
[8, 168, 5806] |
[1] |
1 |
[8, 168, 5806] |
50 |
C50 |
41) |
[8, 1078, 186553] |
[1] |
1 |
[8, 1078, 186553] |
50 |
C50 |
42) |
[8, 758, 140113] |
[1] |
2 |
[8, 758, 140113] |
100 |
C10 x C10 |
43) |
[8, 822, 163921] |
[1] |
2 |
[8, 822, 163921] |
100 |
C2 x C50 |
44) |
[8, 192, 9166] |
[1] |
1 |
[8, 192, 9166] |
50 |
C50 |
45) |
[8, 554, 69529] |
[1] |
2 |
[8, 554, 69529] |
100 |
C2 x C50 |
46) |
[8, 714, 126937] |
[1] |
2 |
[8, 714, 126937] |
100 |
C10 x C10 |
47) |
[5, 283, 19921] |
[1] |
2 |
[5, 283, 19921] |
100 |
C2 x C50 |
48) |
[5, 181, 7409] |
[5, 5] |
1 |
[5, 181, 7409] |
10 |
C10 |
49) |
[5, 348, 28996] |
[1] |
2 |
[5, 348, 28996] |
100 |
C10 x C10 |
50) |
[5, 1137, 262141] |
[1] |
1 |
[5, 1137, 262141] |
50 |
C5 x C10 |
51) |
[5, 282, 15961] |
[1] |
2 |
[5, 282, 15961] |
100 |
C2 x C50 |
52) |
[5, 753, 140701] |
[1] |
1 |
[5, 753, 140701] |
50 |
C50 |
53) |
[5, 1397, 486541] |
[1] |
2 |
[5, 1397, 486541] |
100 |
C2 x C50 |
54) |
[5, 601, 79489] |
[1] |
1 |
[5, 601, 79489] |
50 |
C5 x C10 |
55) |
[5, 323, 21121] |
[1] |
2 |
[5, 323, 21121] |
100 |
C100 |
56) |
[5, 841, 149809] |
[1] |
1 |
[5, 841, 149809] |
50 |
C50 |
57) |
[5, 1253, 325801] |
[1] |
2 |
[5, 1253, 325801] |
100 |
C2 x C50 |
58) |
[5, 502, 60121] |
[1] |
1 |
[5, 502, 60121] |
50 |
C50 |
59) |
[5, 1201, 290389] |
[1] |
1 |
[5, 1201, 290389] |
50 |
C50 |
60) |
[5, 1601, 628549] |
[1] |
1 |
[5, 1601, 628549] |
50 |
C50 |
61) |
[5, 363, 32881] |
[1] |
2 |
[5, 363, 32881] |
100 |
C2 x C50 |
62) |
[5, 806, 161129] |
[1] |
1 |
[5, 806, 161129] |
50 |
C50 |
63) |
[5, 404, 40084] |
[1] |
2 |
[5, 404, 40084] |
100 |
C10 x C10 |
64) |
[5, 898, 171181] |
[1] |
1 |
[5, 898, 171181] |
50 |
C50 |
65) |
[5, 1269, 364309] |
[1] |
1 |
[5, 1269, 364309] |
50 |
C5 x C10 |
66) |
[5, 1369, 461509] |
[1] |
1 |
[5, 1369, 461509] |
50 |
C50 |
67) |
[5, 1341, 373309] |
[1] |
1 |
[5, 1341, 373309] |
50 |
C50 |
68) |
[5, 1326, 416449] |
[1] |
2 |
[5, 1326, 416449] |
100 |
C10 x C10 |
69) |
[5, 1401, 439189] |
[1] |
1 |
[5, 1401, 439189] |
50 |
C5 x C10 |
70) |
[5, 166, 5609] |
[5, 5] |
1 |
[5, 166, 5609] |
10 |
C10 |
71) |
[5, 997, 227701] |
[1] |
1 |
[5, 997, 227701] |
50 |
C50 |
72) |
[5, 1121, 266629] |
[1] |
1 |
[5, 1121, 266629] |
50 |
C50 |
73) |
[5, 513, 62281] |
[1] |
1 |
[5, 513, 62281] |
50 |
C50 |
74) |
[5, 428, 45076] |
[1] |
2 |
[5, 428, 45076] |
100 |
C2 x C50 |
75) |
[5, 459, 52609] |
[1] |
2 |
[5, 459, 52609] |
100 |
C100 |
76) |
[5, 818, 152701] |
[1] |
1 |
[5, 818, 152701] |
50 |
C50 |
77) |
[29, 486, 47449] |
[1] |
1 |
[29, 486, 47449] |
50 |
C50 |
78) |
[29, 1161, 184549] |
[1] |
1 |
[29, 1161, 184549] |
50 |
C50 |
79) |
[29, 300, 15076] |
[1] |
2 |
[29, 300, 15076] |
100 |
C5 x C20 |
80) |
[92, 92, 1909] |
[1] |
2 |
[92, 92, 1909] |
100 |
C2 x C50 |
81) |
[92, 108, 2893] |
[1] |
2 |
[92, 108, 2893] |
100 |
C10 x C10 |
82) |
[193, 895, 43492] |
[1] |
1 |
[193, 895, 43492] |
50 |
C50 |
83) |
[124, 994, 28273] |
[1] |
2 |
[124, 994, 28273] |
100 |
C2 x C50 |
84) |
[905, 33, 46] |
[1] |
1 |
[905, 33, 46] |
200 |
C200 |
85) |
[93, 209, 10897] |
[1] |
1 |
[93, 209, 10897] |
50 |
C5 x C10 |
86) |
[2501, 681, 100309] |
[1] |
1 |
[2501, 681, 100309] |
200 |
C5 x C40 |
87) |
[24, 190, 8161] |
[1] |
1 |
[24, 190, 8161] |
50 |
C50 |
88) |
[24, 1156, 216484] |
[1] |
2 |
[24, 1156, 216484] |
100 |
C2 x C50 |
89) |
[24, 178, 5521] |
[1] |
2 |
[24, 178, 5521] |
100 |
C2 x C50 |
90) |
[24, 382, 13417] |
[1] |
2 |
[24, 382, 13417] |
100 |
C2 x C50 |
91) |
[221, 513, 49825] |
[1] |
1 |
[221, 513, 49825] |
100 |
C100 |
92) |
[893, 39, 157] |
[1] |
2 |
[893, 39, 157] |
100 |
C2 x C50 |
93) |
[428, 60, 472] |
[1] |
1 |
[428, 60, 472] |
50 |
C50 |
94) |
[40, 886, 22009] |
[1] |
1 |
[40, 886, 22009] |
100 |
C100 |
95) |
[40, 186, 7649] |
[1] |
1 |
[40, 186, 7649] |
100 |
C10 x C10 |
96) |
[40, 466, 25129] |
[1] |
1 |
[40, 466, 25129] |
100 |
C100 |
97) |
[40, 178, 2161] |
[1] |
2 |
[40, 178, 2161] |
200 |
C2 x C100 |
98) |
[40, 274, 13009] |
[1] |
2 |
[40, 274, 13009] |
200 |
C2 x C100 |
99) |
[40, 138, 2801] |
[1] |
1 |
[40, 138, 2801] |
100 |
C2 x C50 |
100) |
[149, 961, 21349] |
[1] |
1 |
[149, 961, 21349] |
50 |
C50 |
101) |
[140, 976, 25204] |
[1] |
2 |
[140, 976, 25204] |
200 |
C2 x C100 |
102) |
[140, 188, 3796] |
[1] |
2 |
[140, 188, 3796] |
200 |
C2 x C100 |
103) |
[140, 192, 5716] |
[1] |
2 |
[140, 192, 5716] |
200 |
C10 x C20 |
104) |
[113, 1015, 43732] |
[1] |
2 |
[113, 1015, 43732] |
100 |
C100 |
105) |
[113, 1127, 274564] |
[1] |
1 |
[113, 1127, 274564] |
50 |
C50 |
106) |
[185, 114, 2509] |
[1] |
1 |
[185, 114, 2509] |
100 |
C100 |
107) |
[185, 178, 1261] |
[1] |
1 |
[185, 178, 1261] |
100 |
C100 |
108) |
[89, 966, 90889] |
[1] |
1 |
[89, 966, 90889] |
50 |
C50 |
109) |
[305, 951, 97924] |
[1] |
1 |
[305, 951, 97924] |
100 |
C100 |
110) |
[53, 1070, 95425] |
[1] |
2 |
[53, 1070, 95425] |
100 |
C2 x C50 |
111) |
[53, 229, 13097] |
[1] |
1 |
[53, 229, 13097] |
50 |
C50 |
112) |
[332, 62, 214] |
[1] |
1 |
[332, 62, 214] |
50 |
C50 |
113) |
[2833, 487, 1924] |
[1] |
1 |
[2833, 487, 1924] |
50 |
C50 |
114) |
[785, 89, 214] |
[1] |
1 |
[785, 89, 214] |
300 |
C300 |
115) |
[28, 262, 4813] |
[1] |
2 |
[28, 262, 4813] |
100 |
C100 |
116) |
[28, 202, 3901] |
[1] |
2 |
[28, 202, 3901] |
100 |
C2 x C50 |
117) |
[28, 268, 8884] |
[1] |
2 |
[28, 268, 8884] |
100 |
C100 |
118) |
[412, 350, 30213] |
[1] |
2 |
[412, 350, 30213] |
100 |
C100 |
119) |
[1249, 293, 21150] |
[1] |
1 |
[1249, 293, 21150] |
50 |
C50 |
120) |
[17, 1158, 203593] |
[1] |
1 |
[17, 1158, 203593] |
50 |
C50 |
121) |
[17, 1126, 160297] |
[1] |
1 |
[17, 1126, 160297] |
50 |
C50 |
122) |
[17, 995, 238900] |
[1] |
2 |
[17, 995, 238900] |
100 |
C5 x C20 |
123) |
[17, 299, 22244] |
[1] |
1 |
[17, 299, 22244] |
50 |
C50 |
124) |
[17, 1727, 744676] |
[1] |
1 |
[17, 1727, 744676] |
50 |
C50 |
125) |
[17, 915, 208792] |
[1] |
1 |
[17, 915, 208792] |
50 |
C50 |
126) |
[17, 252, 9076] |
[1] |
2 |
[17, 252, 9076] |
100 |
C2 x C50 |
127) |
[17, 1515, 568600] |
[1] |
2 |
[17, 1515, 568600] |
100 |
C2 x C50 |
128) |
[17, 450, 50557] |
[1] |
1 |
[17, 450, 50557] |
50 |
C50 |
129) |
[17, 1255, 346900] |
[1] |
2 |
[17, 1255, 346900] |
100 |
C100 |
130) |
[1868, 1002, 243529] |
[1] |
1 |
[1868, 1002, 243529] |
50 |
C50 |
131) |
[1112, 802, 673] |
[1] |
2 |
[1112, 802, 673] |
100 |
C10 x C10 |
132) |
[1112, 990, 110473] |
[1] |
2 |
[1112, 990, 110473] |
100 |
C2 x C50 |
133) |
[77, 193, 8369] |
[1] |
1 |
[77, 193, 8369] |
50 |
C50 |
134) |
[77, 260, 5812] |
[1] |
2 |
[77, 260, 5812] |
100 |
C2 x C50 |
135) |
[77, 985, 30325] |
[1] |
2 |
[77, 985, 30325] |
100 |
C2 x C50 |
136) |
[77, 282, 12181] |
[1] |
1 |
[77, 282, 12181] |
50 |
C5 x C10 |
137) |
[77, 897, 119821] |
[1] |
2 |
[77, 897, 119821] |
100 |
C10 x C10 |
138) |
[77, 213, 11169] |
[1] |
2 |
[77, 213, 11169] |
100 |
C2 x C50 |
139) |
[188, 422, 17449] |
[1] |
1 |
[188, 422, 17449] |
50 |
C5 x C10 |
140) |
[44, 946, 65329] |
[1] |
1 |
[44, 946, 65329] |
50 |
C50 |
141) |
[44, 286, 20053] |
[1] |
2 |
[44, 286, 20053] |
100 |
C10 x C10 |
142) |
[44, 70, 1126] |
[1] |
1 |
[44, 70, 1126] |
50 |
C5 x C10 |
143) |
[44, 1106, 147409] |
[1] |
1 |
[44, 1106, 147409] |
50 |
C50 |
144) |
[337, 403, 3448] |
[1] |
1 |
[337, 403, 3448] |
50 |
C50 |
145) |
[1292, 734, 30037] |
[1] |
2 |
[1292, 734, 30037] |
400 |
C2 x C200 |
146) |
[12, 622, 63013] |
[1] |
2 |
[12, 622, 63013] |
100 |
C2 x C50 |
147) |
[12, 178, 7489] |
[1] |
1 |
[12, 178, 7489] |
50 |
C50 |
148) |
[12, 418, 37333] |
[1] |
2 |
[12, 418, 37333] |
100 |
C10 x C10 |
149) |
[12, 430, 46117] |
[1] |
2 |
[12, 430, 46117] |
100 |
C2 x C50 |
150) |
[12, 238, 7249] |
[1] |
1 |
[12, 238, 7249] |
50 |
C50 |
151) |
[21, 649, 74173] |
[1] |
2 |
[21, 649, 74173] |
100 |
C2 x C50 |
152) |
[21, 529, 55213] |
[1] |
1 |
[21, 529, 55213] |
50 |
C50 |
153) |
[21, 925, 126541] |
[1] |
1 |
[21, 925, 126541] |
50 |
C50 |
154) |
[21, 409, 12289] |
[1] |
1 |
[21, 409, 12289] |
50 |
C50 |
155) |
[21, 244, 6484] |
[1] |
2 |
[21, 244, 6484] |
100 |
C10 x C10 |
156) |
[21, 745, 34381] |
[1] |
1 |
[21, 745, 34381] |
50 |
C5 x C10 |
157) |
[85, 153, 3281] |
[1] |
1 |
[85, 153, 3281] |
100 |
C100 |
158) |
[277, 605, 24957] |
[1] |
1 |
[277, 605, 24957] |
50 |
C50 |
159) |
[73, 895, 163300] |
[1] |
2 |
[73, 895, 163300] |
100 |
C2 x C50 |
160) |
[56, 564, 68548] |
[1] |
2 |
[56, 564, 68548] |
100 |
C10 x C10 |
161) |
[56, 554, 52033] |
[1] |
1 |
[56, 554, 52033] |
50 |
C50 |
162) |
[56, 570, 78481] |
[1] |
1 |
[56, 570, 78481] |
50 |
C50 |
163) |
[41, 1166, 192289] |
[1] |
1 |
[41, 1166, 192289] |
50 |
C50 |
164) |
[41, 519, 38548] |
[1] |
1 |
[41, 519, 38548] |
50 |
C50 |
165) |
[41, 354, 27229] |
[1] |
1 |
[41, 354, 27229] |
50 |
C50 |
166) |
[201, 82, 877] |
[1] |
1 |
[201, 82, 877] |
50 |
C50 |
167) |
[241, 187, 7236] |
[1] |
1 |
[241, 187, 7236] |
50 |
C50 |
168) |
[1961, 923, 173272] |
[1] |
1 |
[1961, 923, 173272] |
100 |
C100 |
169) |
[397, 57, 713] |
[1] |
1 |
[397, 57, 713] |
50 |
C50 |
170) |
[284, 68, 517] |
[1] |
2 |
[284, 68, 517] |
100 |
C10 x C10 |
171) |
[365, 909, 191149] |
[1] |
1 |
[365, 909, 191149] |
100 |
C5 x C20 |
172) |
[101, 181, 6953] |
[1] |
1 |
[101, 181, 6953] |
50 |
C50 |
173) |
[101, 693, 59437] |
[1] |
2 |
[101, 693, 59437] |
100 |
C100 |
174) |
[3521, 183, 7492] |
[1] |
1 |
[3521, 183, 7492] |
50 |
C50 |
175) |
[481, 205, 766] |
[1] |
1 |
[481, 205, 766] |
100 |
C100 |
176) |
[265, 61, 334] |
[1] |
1 |
[265, 61, 334] |
100 |
C100 |
177) |
[69, 221, 12193] |
[1] |
1 |
[69, 221, 12193] |
50 |
C50 |
178) |
[488, 806, 4297] |
[1] |
1 |
[488, 806, 4297] |
100 |
C2 x C50 |
179) |
[65, 306, 16909] |
[1] |
1 |
[65, 306, 16909] |
100 |
C100 |
180) |
[65, 1431, 496324] |
[1] |
1 |
[65, 1431, 496324] |
100 |
C100 |