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 180 Igusa CM invariants of non-normal (D4) fields: 142
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[236, 74, 838] |
[1] |
1 |
[236, 74, 838] |
90 |
C90 |
2) |
[137, 846, 176737] |
[1] |
1 |
[137, 846, 176737] |
90 |
C90 |
3) |
[137, 1022, 83569] |
[1] |
1 |
[137, 1022, 83569] |
90 |
C90 |
4) |
[88, 210, 10937] |
[1] |
1 |
[88, 210, 10937] |
90 |
C90 |
5) |
[88, 358, 28873] |
[1] |
1 |
[88, 358, 28873] |
90 |
C90 |
6) |
[88, 886, 41017] |
[1] |
1 |
[88, 886, 41017] |
90 |
C90 |
7) |
[1137, 715, 2452] |
[1] |
1 |
[1137, 715, 2452] |
90 |
C90 |
8) |
[104, 272, 10072] |
[1] |
1 |
[104, 272, 10072] |
180 |
C180 |
9) |
[104, 626, 74569] |
[1] |
1 |
[104, 626, 74569] |
180 |
C180 |
10) |
[1049, 1055, 87076] |
[1] |
1 |
[1049, 1055, 87076] |
90 |
C90 |
11) |
[97, 49, 382] |
[1] |
1 |
[97, 49, 382] |
90 |
C90 |
12) |
[57, 1543, 558148] |
[1] |
1 |
[57, 1543, 558148] |
90 |
C90 |
13) |
[13, 93, 2081] |
[5, 5] |
1 |
[13, 93, 2081] |
15 |
C15 |
14) |
[8, 686, 117137] |
[1] |
1 |
[8, 686, 117137] |
90 |
C90 |
15) |
[8, 1878, 881593] |
[1] |
1 |
[8, 1878, 881593] |
90 |
C90 |
16) |
[8, 1686, 706777] |
[1] |
1 |
[8, 1686, 706777] |
90 |
C90 |
17) |
[8, 1682, 691081] |
[1] |
1 |
[8, 1682, 691081] |
90 |
C90 |
18) |
[8, 698, 61249] |
[1] |
1 |
[8, 698, 61249] |
90 |
C90 |
19) |
[8, 638, 55553] |
[1] |
1 |
[8, 638, 55553] |
90 |
C90 |
20) |
[8, 1250, 378457] |
[1] |
1 |
[8, 1250, 378457] |
90 |
C90 |
21) |
[8, 1294, 243377] |
[1] |
1 |
[8, 1294, 243377] |
90 |
C90 |
22) |
[8, 1878, 880921] |
[1] |
1 |
[8, 1878, 880921] |
90 |
C90 |
23) |
[8, 426, 43057] |
[1] |
1 |
[8, 426, 43057] |
90 |
C90 |
24) |
[8, 224, 12526] |
[1] |
1 |
[8, 224, 12526] |
90 |
C3 x C30 |
25) |
[8, 1542, 572809] |
[1] |
1 |
[8, 1542, 572809] |
90 |
C90 |
26) |
[8, 1298, 333001] |
[1] |
1 |
[8, 1298, 333001] |
90 |
C90 |
27) |
[8, 1410, 430777] |
[1] |
1 |
[8, 1410, 430777] |
90 |
C90 |
28) |
[8, 1618, 653833] |
[1] |
1 |
[8, 1618, 653833] |
90 |
C90 |
29) |
[5, 1361, 429049] |
[1] |
1 |
[5, 1361, 429049] |
90 |
C90 |
30) |
[5, 1769, 744929] |
[1] |
1 |
[5, 1769, 744929] |
90 |
C90 |
31) |
[5, 214, 11369] |
[4, 4] |
1 |
[5, 214, 11369] |
15 |
C15 |
32) |
[5, 1737, 745261] |
[1] |
1 |
[5, 1737, 745261] |
90 |
C90 |
33) |
[5, 1797, 804301] |
[1] |
1 |
[5, 1797, 804301] |
90 |
C90 |
34) |
[5, 1454, 528449] |
[1] |
1 |
[5, 1454, 528449] |
90 |
C90 |
35) |
[5, 1377, 449881] |
[1] |
1 |
[5, 1377, 449881] |
90 |
C90 |
36) |
[5, 1941, 899089] |
[1] |
1 |
[5, 1941, 899089] |
90 |
C90 |
37) |
[5, 1429, 503849] |
[1] |
1 |
[5, 1429, 503849] |
90 |
C90 |
38) |
[5, 1457, 527201] |
[1] |
1 |
[5, 1457, 527201] |
90 |
C90 |
39) |
[5, 1446, 468649] |
[1] |
1 |
[5, 1446, 468649] |
90 |
C90 |
40) |
[5, 1541, 550889] |
[1] |
1 |
[5, 1541, 550889] |
90 |
C90 |
41) |
[5, 1941, 941869] |
[1] |
1 |
[5, 1941, 941869] |
90 |
C3 x C30 |
42) |
[5, 1177, 313121] |
[1] |
1 |
[5, 1177, 313121] |
90 |
C90 |
43) |
[5, 1357, 459161] |
[1] |
1 |
[5, 1357, 459161] |
90 |
C90 |
44) |
[5, 49, 569] |
[5, 25] |
1 |
[5, 49, 569] |
3 |
C3 |
45) |
[5, 1198, 329921] |
[1] |
1 |
[5, 1198, 329921] |
90 |
C90 |
46) |
[5, 1781, 706529] |
[1] |
1 |
[5, 1781, 706529] |
90 |
C90 |
47) |
[5, 969, 227329] |
[1] |
1 |
[5, 969, 227329] |
90 |
C90 |
48) |
[5, 2126, 1001969] |
[1] |
1 |
[5, 2126, 1001969] |
90 |
C90 |
49) |
[5, 1201, 351569] |
[1] |
1 |
[5, 1201, 351569] |
90 |
C90 |
50) |
[5, 1254, 391849] |
[1] |
1 |
[5, 1254, 391849] |
90 |
C90 |
51) |
[5, 1409, 436369] |
[1] |
1 |
[5, 1409, 436369] |
90 |
C90 |
52) |
[5, 158, 5521] |
[6, 6] |
1 |
[5, 158, 5521] |
15 |
C15 |
53) |
[29, 1385, 471661] |
[1] |
1 |
[29, 1385, 471661] |
90 |
C90 |
54) |
[29, 417, 21541] |
[1] |
1 |
[29, 417, 21541] |
90 |
C90 |
55) |
[29, 1469, 498709] |
[1] |
1 |
[29, 1469, 498709] |
90 |
C90 |
56) |
[29, 166, 5033] |
[2, 2] |
1 |
[29, 166, 5033] |
30 |
C30 |
57) |
[92, 930, 171697] |
[1] |
1 |
[92, 930, 171697] |
90 |
C90 |
58) |
[92, 762, 108361] |
[1] |
1 |
[92, 762, 108361] |
90 |
C90 |
59) |
[905, 1071, 96484] |
[1] |
1 |
[905, 1071, 96484] |
360 |
C360 |
60) |
[849, 538, 41797] |
[1] |
1 |
[849, 538, 41797] |
90 |
C90 |
61) |
[93, 697, 65629] |
[1] |
1 |
[93, 697, 65629] |
90 |
C90 |
62) |
[24, 146, 5113] |
[3, 3] |
1 |
[24, 146, 5113] |
30 |
C30 |
63) |
[24, 130, 2281] |
[3, 3] |
1 |
[24, 130, 2281] |
30 |
C30 |
64) |
[24, 226, 12553] |
[1] |
1 |
[24, 226, 12553] |
90 |
C90 |
65) |
[257, 1271, 333892] |
[1] |
1 |
[257, 1271, 333892] |
270 |
C3 x C90 |
66) |
[428, 66, 982] |
[1] |
1 |
[428, 66, 982] |
90 |
C90 |
67) |
[2249, 735, 40036] |
[1] |
1 |
[2249, 735, 40036] |
360 |
C360 |
68) |
[40, 234, 13649] |
[1] |
1 |
[40, 234, 13649] |
180 |
C2 x C90 |
69) |
[149, 293, 10697] |
[1] |
1 |
[149, 293, 10697] |
90 |
C3 x C30 |
70) |
[908, 978, 6673] |
[1] |
1 |
[908, 978, 6673] |
90 |
C3 x C30 |
71) |
[509, 1689, 713053] |
[1] |
1 |
[509, 1689, 713053] |
90 |
C90 |
72) |
[113, 1623, 643588] |
[1] |
1 |
[113, 1623, 643588] |
90 |
C90 |
73) |
[248, 730, 23857] |
[1] |
1 |
[248, 730, 23857] |
90 |
C3 x C30 |
74) |
[89, 429, 45454] |
[1] |
1 |
[89, 429, 45454] |
90 |
C90 |
75) |
[89, 1679, 694948] |
[1] |
1 |
[89, 1679, 694948] |
90 |
C90 |
76) |
[89, 599, 31828] |
[1] |
1 |
[89, 599, 31828] |
90 |
C90 |
77) |
[533, 750, 4177] |
[1] |
1 |
[533, 750, 4177] |
180 |
C2 x C90 |
78) |
[689, 534, 27193] |
[1] |
1 |
[689, 534, 27193] |
360 |
C360 |
79) |
[53, 1021, 97357] |
[1] |
1 |
[53, 1021, 97357] |
90 |
C90 |
80) |
[53, 278, 5753] |
[2, 2] |
1 |
[53, 278, 5753] |
30 |
C30 |
81) |
[53, 341, 25241] |
[1] |
1 |
[53, 341, 25241] |
90 |
C3 x C30 |
82) |
[53, 617, 60709] |
[1] |
1 |
[53, 617, 60709] |
90 |
C90 |
83) |
[61, 213, 10961] |
[1] |
1 |
[61, 213, 10961] |
90 |
C90 |
84) |
[1461, 1213, 367477] |
[1] |
1 |
[1461, 1213, 367477] |
90 |
C90 |
85) |
[965, 981, 8749] |
[1] |
1 |
[965, 981, 8749] |
180 |
C180 |
86) |
[17, 1443, 491284] |
[1] |
1 |
[17, 1443, 491284] |
90 |
C90 |
87) |
[17, 1026, 72157] |
[1] |
1 |
[17, 1026, 72157] |
90 |
C90 |
88) |
[17, 1878, 880633] |
[1] |
1 |
[17, 1878, 880633] |
90 |
C90 |
89) |
[17, 278, 12521] |
[1] |
1 |
[17, 278, 12521] |
90 |
C90 |
90) |
[17, 278, 12521] |
[2, 2] |
1 |
[17, 278, 12521] |
90 |
C90 |
91) |
[17, 118, 3209] |
[4, 4] |
1 |
[17, 118, 3209] |
45 |
C45 |
92) |
[17, 1806, 815137] |
[1] |
1 |
[17, 1806, 815137] |
90 |
C90 |
93) |
[17, 1758, 765841] |
[1] |
1 |
[17, 1758, 765841] |
90 |
C90 |
94) |
[17, 1251, 385432] |
[1] |
1 |
[17, 1251, 385432] |
90 |
C90 |
95) |
[3065, 399, 20644] |
[1] |
1 |
[3065, 399, 20644] |
180 |
C180 |
96) |
[773, 1473, 509773] |
[1] |
1 |
[773, 1473, 509773] |
90 |
C90 |
97) |
[653, 1577, 608509] |
[1] |
1 |
[653, 1577, 608509] |
90 |
C90 |
98) |
[653, 173, 3401] |
[1] |
1 |
[653, 173, 3401] |
90 |
C90 |
99) |
[44, 1266, 330289] |
[1] |
1 |
[44, 1266, 330289] |
90 |
C90 |
100) |
[44, 954, 206233] |
[1] |
1 |
[44, 954, 206233] |
90 |
C90 |
101) |
[44, 1546, 557929] |
[1] |
1 |
[44, 1546, 557929] |
90 |
C90 |
102) |
[1985, 807, 19396] |
[1] |
1 |
[1985, 807, 19396] |
180 |
C180 |
103) |
[1985, 947, 219736] |
[1] |
1 |
[1985, 947, 219736] |
180 |
C180 |
104) |
[12, 1526, 167017] |
[1] |
1 |
[12, 1526, 167017] |
90 |
C90 |
105) |
[12, 622, 34513] |
[1] |
1 |
[12, 622, 34513] |
90 |
C90 |
106) |
[12, 1138, 173233] |
[1] |
1 |
[12, 1138, 173233] |
90 |
C90 |
107) |
[12, 1090, 204097] |
[1] |
1 |
[12, 1090, 204097] |
90 |
C90 |
108) |
[12, 1070, 135697] |
[1] |
1 |
[12, 1070, 135697] |
90 |
C90 |
109) |
[12, 1318, 341353] |
[1] |
1 |
[12, 1318, 341353] |
90 |
C90 |
110) |
[12, 638, 94849] |
[1] |
1 |
[12, 638, 94849] |
90 |
C90 |
111) |
[12, 1078, 288793] |
[1] |
1 |
[12, 1078, 288793] |
90 |
C90 |
112) |
[12, 1154, 176977] |
[1] |
1 |
[12, 1154, 176977] |
90 |
C90 |
113) |
[12, 430, 45457] |
[1] |
1 |
[12, 430, 45457] |
90 |
C90 |
114) |
[21, 1165, 203221] |
[1] |
1 |
[21, 1165, 203221] |
90 |
C3 x C30 |
115) |
[21, 1285, 338461] |
[1] |
1 |
[21, 1285, 338461] |
90 |
C90 |
116) |
[21, 206, 10273] |
[2, 2] |
1 |
[21, 206, 10273] |
30 |
C30 |
117) |
[21, 430, 43201] |
[1] |
1 |
[21, 430, 43201] |
90 |
C90 |
118) |
[21, 1069, 124909] |
[1] |
1 |
[21, 1069, 124909] |
90 |
C90 |
119) |
[85, 601, 35029] |
[1] |
1 |
[85, 601, 35029] |
180 |
C180 |
120) |
[85, 213, 11321] |
[1] |
1 |
[85, 213, 11321] |
180 |
C2 x C90 |
121) |
[233, 285, 10462] |
[1] |
1 |
[233, 285, 10462] |
90 |
C90 |
122) |
[56, 858, 154417] |
[1] |
1 |
[56, 858, 154417] |
90 |
C90 |
123) |
[41, 935, 214036] |
[1] |
1 |
[41, 935, 214036] |
90 |
C90 |
124) |
[41, 83, 1220] |
[5] |
1 |
[41, 83, 1220] |
18 |
C18 |
125) |
[41, 83, 1220] |
[2, 10] |
1 |
[41, 83, 1220] |
18 |
C18 |
126) |
[41, 1566, 596689] |
[1] |
1 |
[41, 1566, 596689] |
90 |
C90 |
127) |
[41, 1839, 843748] |
[1] |
1 |
[41, 1839, 843748] |
90 |
C90 |
128) |
[41, 386, 35773] |
[1] |
1 |
[41, 386, 35773] |
90 |
C90 |
129) |
[365, 837, 6421] |
[1] |
1 |
[365, 837, 6421] |
180 |
C2 x C90 |
130) |
[365, 301, 21829] |
[1] |
1 |
[365, 301, 21829] |
180 |
C180 |
131) |
[101, 449, 49769] |
[1] |
1 |
[101, 449, 49769] |
90 |
C3 x C30 |
132) |
[101, 641, 51589] |
[1] |
1 |
[101, 641, 51589] |
90 |
C90 |
133) |
[101, 13, 17] |
[25] |
1 |
[101, 13, 17] |
3 |
C3 |
134) |
[65, 1767, 775876] |
[1] |
1 |
[65, 1767, 775876] |
180 |
C180 |
135) |
[65, 1091, 264664] |
[1] |
1 |
[65, 1091, 264664] |
180 |
C180 |
136) |
[65, 309, 19174] |
[1] |
1 |
[65, 309, 19174] |
180 |
C180 |
137) |
[65, 118, 2441] |
[1] |
1 |
[65, 118, 2441] |
180 |
C2 x C90 |
138) |
[65, 1182, 223441] |
[1] |
1 |
[65, 1182, 223441] |
180 |
C2 x C90 |
139) |
[65, 1686, 694009] |
[1] |
1 |
[65, 1686, 694009] |
180 |
C180 |
140) |
[65, 354, 31069] |
[1] |
1 |
[65, 354, 31069] |
180 |
C2 x C90 |
141) |
[65, 1367, 449476] |
[1] |
1 |
[65, 1367, 449476] |
180 |
C180 |
142) |
[65, 118, 2441] |
[2, 2] |
1 |
[65, 118, 2441] |
180 |
C2 x C90 |