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 18 Igusa CM invariants of non-normal (D4) fields: 170
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[157, 102, 89] |
[1] |
1 |
[157, 102, 89] |
9 |
C9 |
2) |
[809, 103, 832] |
[1] |
1 |
[809, 103, 832] |
9 |
C9 |
3) |
[2689, 63, 320] |
[1] |
1 |
[2689, 63, 320] |
9 |
C9 |
4) |
[10909, 153, 3125] |
[1] |
1 |
[10909, 153, 3125] |
45 |
C45 |
5) |
[137, 143, 4804] |
[1] |
1 |
[137, 143, 4804] |
9 |
C9 |
6) |
[3889, 63, 20] |
[1] |
1 |
[3889, 63, 20] |
27 |
C3 x C9 |
7) |
[109, 153, 5825] |
[1] |
1 |
[109, 153, 5825] |
9 |
C9 |
8) |
[109, 217, 3897] |
[1] |
1 |
[109, 217, 3897] |
9 |
C9 |
9) |
[641, 29, 50] |
[1] |
1 |
[641, 29, 50] |
9 |
C9 |
10) |
[3061, 109, 2205] |
[1] |
1 |
[3061, 109, 2205] |
9 |
C9 |
11) |
[3769, 67, 180] |
[1] |
1 |
[3769, 67, 180] |
9 |
C9 |
12) |
[7489, 87, 20] |
[1] |
1 |
[7489, 87, 20] |
9 |
C9 |
13) |
[821, 169, 2009] |
[1] |
1 |
[821, 169, 2009] |
9 |
C9 |
14) |
[13, 257, 5953] |
[1] |
1 |
[13, 257, 5953] |
9 |
C9 |
15) |
[13, 57, 809] |
[1] |
1 |
[13, 57, 809] |
9 |
C9 |
16) |
[13, 133, 2989] |
[1] |
2 |
[13, 133, 2989] |
18 |
C18 |
17) |
[13, 49, 337] |
[2, 2] |
1 |
[13, 49, 337] |
9 |
C9 |
18) |
[13, 37, 313] |
[1] |
1 |
[13, 37, 313] |
9 |
C9 |
19) |
[13, 149, 5521] |
[1] |
1 |
[13, 149, 5521] |
9 |
C9 |
20) |
[13, 197, 3121] |
[1] |
1 |
[13, 197, 3121] |
9 |
C9 |
21) |
[13, 245, 6553] |
[1] |
1 |
[13, 245, 6553] |
9 |
C9 |
22) |
[13, 49, 337] |
[1] |
1 |
[13, 49, 337] |
9 |
C9 |
23) |
[13, 125, 2473] |
[1] |
1 |
[13, 125, 2473] |
9 |
C9 |
24) |
[1741, 170, 261] |
[1] |
1 |
[1741, 170, 261] |
9 |
C9 |
25) |
[8, 194, 8761] |
[1] |
1 |
[8, 194, 8761] |
9 |
C9 |
26) |
[8, 278, 18169] |
[1] |
1 |
[8, 278, 18169] |
9 |
C9 |
27) |
[8, 122, 2753] |
[1] |
1 |
[8, 122, 2753] |
9 |
C9 |
28) |
[8, 58, 769] |
[1] |
1 |
[8, 58, 769] |
9 |
C9 |
29) |
[8, 330, 18513] |
[1] |
4 |
[8, 330, 18513] |
36 |
C2 x C18 |
30) |
[8, 62, 929] |
[1] |
1 |
[8, 62, 929] |
9 |
C9 |
31) |
[8, 134, 4201] |
[1] |
1 |
[8, 134, 4201] |
9 |
C9 |
32) |
[8, 262, 12553] |
[1] |
1 |
[8, 262, 12553] |
9 |
C9 |
33) |
[8, 194, 9337] |
[1] |
1 |
[8, 194, 9337] |
9 |
C9 |
34) |
[8, 150, 4057] |
[1] |
1 |
[8, 150, 4057] |
9 |
C9 |
35) |
[8, 174, 7281] |
[1] |
2 |
[8, 174, 7281] |
18 |
C18 |
36) |
[8, 198, 8233] |
[1] |
1 |
[8, 198, 8233] |
9 |
C9 |
37) |
[8, 182, 7993] |
[1] |
1 |
[8, 182, 7993] |
9 |
C9 |
38) |
[8, 90, 1993] |
[1] |
2 |
[8, 90, 1993] |
18 |
C18 |
39) |
[8, 130, 4153] |
[1] |
1 |
[8, 130, 4153] |
9 |
C9 |
40) |
[8, 182, 7129] |
[1] |
1 |
[8, 182, 7129] |
9 |
C9 |
41) |
[8, 162, 6361] |
[1] |
1 |
[8, 162, 6361] |
9 |
C9 |
42) |
[8, 154, 4961] |
[1] |
2 |
[8, 154, 4961] |
18 |
C18 |
43) |
[8, 106, 2417] |
[1] |
1 |
[8, 106, 2417] |
9 |
C9 |
44) |
[8, 150, 5113] |
[1] |
1 |
[8, 150, 5113] |
9 |
C9 |
45) |
[8, 58, 641] |
[1] |
1 |
[8, 58, 641] |
9 |
C9 |
46) |
[8, 94, 2081] |
[1] |
1 |
[8, 94, 2081] |
9 |
C9 |
47) |
[8, 258, 16633] |
[1] |
1 |
[8, 258, 16633] |
9 |
C9 |
48) |
[8, 114, 3049] |
[1] |
1 |
[8, 114, 3049] |
9 |
C9 |
49) |
[5, 237, 12681] |
[1] |
2 |
[5, 237, 12681] |
18 |
C18 |
50) |
[5, 246, 14409] |
[1] |
2 |
[5, 246, 14409] |
18 |
C18 |
51) |
[5, 134, 3769] |
[1] |
1 |
[5, 134, 3769] |
9 |
C9 |
52) |
[5, 189, 8269] |
[1] |
1 |
[5, 189, 8269] |
9 |
C9 |
53) |
[5, 206, 10289] |
[1] |
1 |
[5, 206, 10289] |
9 |
C9 |
54) |
[5, 381, 34929] |
[1] |
2 |
[5, 381, 34929] |
18 |
C18 |
55) |
[5, 177, 7281] |
[1] |
2 |
[5, 177, 7281] |
18 |
C18 |
56) |
[5, 109, 2689] |
[1] |
1 |
[5, 109, 2689] |
9 |
C9 |
57) |
[5, 229, 12829] |
[1] |
1 |
[5, 229, 12829] |
9 |
C9 |
58) |
[5, 153, 5701] |
[1] |
1 |
[5, 153, 5701] |
9 |
C9 |
59) |
[5, 126, 3889] |
[1] |
1 |
[5, 126, 3889] |
9 |
C9 |
60) |
[5, 47, 541] |
[1] |
2 |
[5, 47, 541] |
18 |
C18 |
61) |
[5, 209, 10909] |
[1] |
1 |
[5, 209, 10909] |
9 |
C9 |
62) |
[5, 138, 4261] |
[1] |
1 |
[5, 138, 4261] |
9 |
C9 |
63) |
[5, 153, 5821] |
[1] |
1 |
[5, 153, 5821] |
9 |
C9 |
64) |
[5, 174, 7489] |
[1] |
1 |
[5, 174, 7489] |
9 |
C9 |
65) |
[5, 741, 135369] |
[1] |
4 |
[5, 741, 135369] |
36 |
C2 x C18 |
66) |
[5, 201, 10069] |
[1] |
1 |
[5, 201, 10069] |
9 |
C9 |
67) |
[5, 134, 3769] |
[2, 2] |
1 |
[5, 134, 3769] |
9 |
C9 |
68) |
[5, 226, 12589] |
[1] |
1 |
[5, 226, 12589] |
9 |
C9 |
69) |
[5, 174, 7489] |
[2, 2] |
1 |
[5, 174, 7489] |
9 |
C9 |
70) |
[5, 329, 25529] |
[1] |
2 |
[5, 329, 25529] |
18 |
C18 |
71) |
[5, 269, 17989] |
[1] |
1 |
[5, 269, 17989] |
9 |
C9 |
72) |
[5, 93, 1801] |
[1] |
1 |
[5, 93, 1801] |
9 |
C9 |
73) |
[5, 209, 9209] |
[1] |
1 |
[5, 209, 9209] |
9 |
C9 |
74) |
[5, 157, 6101] |
[1] |
1 |
[5, 157, 6101] |
9 |
C9 |
75) |
[5, 249, 15349] |
[1] |
1 |
[5, 249, 15349] |
9 |
C9 |
76) |
[5, 46, 449] |
[2, 2] |
1 |
[5, 46, 449] |
3 |
C3 |
77) |
[5, 117, 3061] |
[1] |
1 |
[5, 117, 3061] |
9 |
C9 |
78) |
[5, 269, 16189] |
[1] |
1 |
[5, 269, 16189] |
9 |
C9 |
79) |
[5, 181, 6829] |
[1] |
1 |
[5, 181, 6829] |
9 |
C9 |
80) |
[5, 166, 6569] |
[1] |
1 |
[5, 166, 6569] |
9 |
C9 |
81) |
[5, 261, 14029] |
[1] |
1 |
[5, 261, 14029] |
9 |
C9 |
82) |
[29, 49, 593] |
[1] |
1 |
[29, 49, 593] |
9 |
C9 |
83) |
[29, 221, 3329] |
[1] |
1 |
[29, 221, 3329] |
9 |
C9 |
84) |
[29, 169, 2609] |
[1] |
1 |
[29, 169, 2609] |
9 |
C9 |
85) |
[29, 190, 1601] |
[1] |
1 |
[29, 190, 1601] |
9 |
C9 |
86) |
[29, 122, 2677] |
[1] |
1 |
[29, 122, 2677] |
9 |
C9 |
87) |
[29, 130, 3181] |
[1] |
1 |
[29, 130, 3181] |
9 |
C9 |
88) |
[29, 85, 1741] |
[1] |
1 |
[29, 85, 1741] |
9 |
C9 |
89) |
[941, 33, 37] |
[1] |
1 |
[941, 33, 37] |
9 |
C9 |
90) |
[5701, 101, 1125] |
[1] |
1 |
[5701, 101, 1125] |
9 |
C9 |
91) |
[1613, 41, 17] |
[1] |
1 |
[1613, 41, 17] |
9 |
C9 |
92) |
[6361, 81, 50] |
[1] |
1 |
[6361, 81, 50] |
9 |
C9 |
93) |
[2753, 61, 242] |
[1] |
1 |
[2753, 61, 242] |
9 |
C9 |
94) |
[757, 37, 153] |
[1] |
1 |
[757, 37, 153] |
9 |
C9 |
95) |
[1973, 101, 2057] |
[1] |
1 |
[1973, 101, 2057] |
9 |
C9 |
96) |
[257, 87, 1828] |
[1] |
1 |
[257, 87, 1828] |
27 |
C3 x C9 |
97) |
[257, 66, 61] |
[1] |
1 |
[257, 66, 61] |
27 |
C3 x C9 |
98) |
[877, 149, 3577] |
[1] |
1 |
[877, 149, 3577] |
9 |
C9 |
99) |
[877, 33, 53] |
[1] |
1 |
[877, 33, 53] |
9 |
C9 |
100) |
[1093, 61, 657] |
[1] |
1 |
[1093, 61, 657] |
45 |
C45 |
101) |
[313, 55, 52] |
[1] |
1 |
[313, 55, 52] |
9 |
C9 |
102) |
[313, 55, 52] |
[2] |
1 |
[313, 55, 52] |
9 |
C9 |
103) |
[149, 110, 641] |
[1] |
1 |
[149, 110, 641] |
9 |
C9 |
104) |
[149, 21, 73] |
[1] |
1 |
[149, 21, 73] |
9 |
C9 |
105) |
[1109, 53, 425] |
[1] |
1 |
[1109, 53, 425] |
9 |
C9 |
106) |
[113, 606, 3217] |
[1] |
1 |
[113, 606, 3217] |
9 |
C9 |
107) |
[113, 119, 1252] |
[2] |
1 |
[113, 119, 1252] |
3 |
C3 |
108) |
[857, 159, 964] |
[1] |
1 |
[857, 159, 964] |
9 |
C9 |
109) |
[10069, 157, 3645] |
[1] |
1 |
[10069, 157, 3645] |
27 |
C3 x C9 |
110) |
[89, 78, 97] |
[2] |
1 |
[89, 78, 97] |
3 |
C3 |
111) |
[53, 129, 2557] |
[1] |
1 |
[53, 129, 2557] |
9 |
C9 |
112) |
[53, 133, 593] |
[1] |
1 |
[53, 133, 593] |
9 |
C9 |
113) |
[53, 66, 877] |
[1] |
1 |
[53, 66, 877] |
9 |
C9 |
114) |
[332, 48, 244] |
[1] |
2 |
[332, 48, 244] |
18 |
C18 |
115) |
[5821, 121, 2205] |
[1] |
1 |
[5821, 121, 2205] |
27 |
C3 x C9 |
116) |
[6569, 83, 80] |
[1] |
1 |
[6569, 83, 80] |
9 |
C9 |
117) |
[1373, 145, 4913] |
[1] |
1 |
[1373, 145, 4913] |
27 |
C3 x C9 |
118) |
[37, 101, 2097] |
[1] |
1 |
[37, 101, 2097] |
9 |
C9 |
119) |
[37, 241, 13401] |
[1] |
1 |
[37, 241, 13401] |
9 |
C9 |
120) |
[61, 190, 5121] |
[1] |
1 |
[61, 190, 5121] |
9 |
C9 |
121) |
[61, 33, 257] |
[1] |
1 |
[61, 33, 257] |
9 |
C9 |
122) |
[197, 57, 369] |
[1] |
2 |
[197, 57, 369] |
18 |
C18 |
123) |
[593, 98, 29] |
[1] |
1 |
[593, 98, 29] |
9 |
C9 |
124) |
[17, 103, 2308] |
[2, 2] |
1 |
[17, 103, 2308] |
3 |
C3 |
125) |
[17, 303, 22948] |
[1] |
1 |
[17, 303, 22948] |
9 |
C9 |
126) |
[17, 167, 6628] |
[2] |
1 |
[17, 167, 6628] |
3 |
C3 |
127) |
[17, 74, 757] |
[1] |
1 |
[17, 74, 757] |
9 |
C9 |
128) |
[17, 334, 5857] |
[1] |
1 |
[17, 334, 5857] |
9 |
C9 |
129) |
[17, 319, 24484] |
[1] |
1 |
[17, 319, 24484] |
9 |
C9 |
130) |
[17, 351, 29572] |
[1] |
1 |
[17, 351, 29572] |
9 |
C9 |
131) |
[17, 174, 7297] |
[1] |
1 |
[17, 174, 7297] |
9 |
C9 |
132) |
[17, 106, 1109] |
[1] |
1 |
[17, 106, 1109] |
9 |
C9 |
133) |
[17, 111, 3076] |
[2] |
1 |
[17, 111, 3076] |
3 |
C3 |
134) |
[17, 222, 5521] |
[1] |
1 |
[17, 222, 5521] |
9 |
C9 |
135) |
[17, 78, 1249] |
[2, 2] |
1 |
[17, 78, 1249] |
3 |
C3 |
136) |
[17, 98, 701] |
[1] |
1 |
[17, 98, 701] |
9 |
C9 |
137) |
[17, 262, 7369] |
[1] |
1 |
[17, 262, 7369] |
9 |
C9 |
138) |
[17, 198, 8713] |
[1] |
1 |
[17, 198, 8713] |
9 |
C9 |
139) |
[173, 105, 637] |
[1] |
2 |
[173, 105, 637] |
18 |
C18 |
140) |
[2081, 47, 32] |
[1] |
1 |
[2081, 47, 32] |
45 |
C45 |
141) |
[3049, 57, 50] |
[1] |
1 |
[3049, 57, 50] |
9 |
C9 |
142) |
[701, 49, 425] |
[1] |
1 |
[701, 49, 425] |
9 |
C9 |
143) |
[2473, 139, 4212] |
[1] |
1 |
[2473, 139, 4212] |
9 |
C9 |
144) |
[653, 33, 109] |
[1] |
1 |
[653, 33, 109] |
9 |
C9 |
145) |
[44, 144, 4084] |
[1] |
2 |
[44, 144, 4084] |
18 |
C18 |
146) |
[337, 47, 468] |
[1] |
1 |
[337, 47, 468] |
9 |
C9 |
147) |
[10289, 103, 80] |
[1] |
1 |
[10289, 103, 80] |
9 |
C9 |
148) |
[12, 22, 109] |
[3, 3] |
2 |
[12, 22, 109] |
6 |
C6 |
149) |
[769, 29, 18] |
[1] |
1 |
[769, 29, 18] |
9 |
C9 |
150) |
[277, 21, 41] |
[1] |
1 |
[277, 21, 41] |
9 |
C9 |
151) |
[2417, 53, 98] |
[1] |
1 |
[2417, 53, 98] |
9 |
C9 |
152) |
[1181, 97, 2057] |
[1] |
1 |
[1181, 97, 2057] |
9 |
C9 |
153) |
[73, 42, 149] |
[1] |
1 |
[73, 42, 149] |
9 |
C9 |
154) |
[233, 87, 436] |
[2] |
1 |
[233, 87, 436] |
9 |
C9 |
155) |
[233, 95, 1732] |
[1] |
1 |
[233, 95, 1732] |
9 |
C9 |
156) |
[233, 51, 592] |
[1] |
1 |
[233, 51, 592] |
9 |
C9 |
157) |
[233, 87, 436] |
[1] |
1 |
[233, 87, 436] |
9 |
C9 |
158) |
[3121, 103, 1872] |
[1] |
1 |
[3121, 103, 1872] |
45 |
C45 |
159) |
[7993, 91, 72] |
[1] |
1 |
[7993, 91, 72] |
9 |
C9 |
160) |
[41, 126, 3313] |
[1] |
1 |
[41, 126, 3313] |
9 |
C9 |
161) |
[41, 111, 1348] |
[2] |
1 |
[41, 111, 1348] |
3 |
C3 |
162) |
[41, 135, 3316] |
[2] |
1 |
[41, 135, 3316] |
9 |
C9 |
163) |
[41, 135, 3316] |
[1] |
1 |
[41, 135, 3316] |
9 |
C9 |
164) |
[41, 42, 277] |
[1] |
1 |
[41, 42, 277] |
9 |
C9 |
165) |
[1801, 91, 1620] |
[1] |
1 |
[1801, 91, 1620] |
9 |
C9 |
166) |
[829, 149, 369] |
[1] |
1 |
[829, 149, 369] |
9 |
C9 |
167) |
[9209, 203, 8000] |
[1] |
1 |
[9209, 203, 8000] |
9 |
C9 |
168) |
[353, 39, 292] |
[2] |
1 |
[353, 39, 292] |
3 |
C3 |
169) |
[929, 31, 8] |
[1] |
1 |
[929, 31, 8] |
9 |
C9 |
170) |
[101, 113, 137] |
[1] |
1 |
[101, 113, 137] |
9 |
C9 |