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 200 Igusa CM invariants of non-normal (D4) fields: 161
Number |
Igusa invariants |
Conductor |
Components |
Quartic invariants |
Class number |
Class group |
1) |
[317, 377, 17701] |
[1] |
1 |
[317, 377, 17701] |
100 |
C100 |
2) |
[165, 937, 23101] |
[1] |
1 |
[165, 937, 23101] |
200 |
C2 x C100 |
3) |
[344, 264, 8824] |
[1] |
1 |
[344, 264, 8824] |
100 |
C2 x C50 |
4) |
[809, 1455, 495076] |
[1] |
1 |
[809, 1455, 495076] |
100 |
C100 |
5) |
[437, 885, 12157] |
[1] |
1 |
[437, 885, 12157] |
100 |
C100 |
6) |
[60, 766, 40849] |
[1] |
1 |
[60, 766, 40849] |
200 |
C2 x C2 x C50 |
7) |
[60, 994, 97009] |
[1] |
1 |
[60, 994, 97009] |
200 |
C2 x C10 x C10 |
8) |
[60, 218, 11641] |
[1] |
1 |
[60, 218, 11641] |
200 |
C2 x C100 |
9) |
[60, 562, 38401] |
[1] |
1 |
[60, 562, 38401] |
200 |
C2 x C2 x C50 |
10) |
[60, 334, 24049] |
[1] |
1 |
[60, 334, 24049] |
200 |
C2 x C100 |
11) |
[2729, 575, 76516] |
[1] |
1 |
[2729, 575, 76516] |
100 |
C2 x C50 |
12) |
[385, 211, 10264] |
[1] |
1 |
[385, 211, 10264] |
200 |
C2 x C100 |
13) |
[236, 90, 1966] |
[1] |
1 |
[236, 90, 1966] |
100 |
C2 x C50 |
14) |
[137, 771, 72952] |
[1] |
1 |
[137, 771, 72952] |
100 |
C2 x C50 |
15) |
[137, 1695, 705892] |
[1] |
1 |
[137, 1695, 705892] |
100 |
C10 x C10 |
16) |
[137, 798, 104401] |
[1] |
1 |
[137, 798, 104401] |
100 |
C100 |
17) |
[129, 910, 204961] |
[1] |
1 |
[129, 910, 204961] |
100 |
C2 x C50 |
18) |
[129, 1735, 743236] |
[1] |
1 |
[129, 1735, 743236] |
100 |
C2 x C50 |
19) |
[129, 277, 9862] |
[1] |
1 |
[129, 277, 9862] |
100 |
C2 x C50 |
20) |
[104, 202, 10097] |
[1] |
1 |
[104, 202, 10097] |
200 |
C2 x C2 x C50 |
21) |
[161, 365, 30046] |
[1] |
1 |
[161, 365, 30046] |
100 |
C2 x C50 |
22) |
[161, 1383, 439492] |
[1] |
1 |
[161, 1383, 439492] |
100 |
C100 |
23) |
[249, 1135, 236836] |
[1] |
1 |
[249, 1135, 236836] |
100 |
C100 |
24) |
[109, 201, 10073] |
[1] |
1 |
[109, 201, 10073] |
100 |
C100 |
25) |
[641, 1511, 534724] |
[1] |
1 |
[641, 1511, 534724] |
100 |
C100 |
26) |
[57, 1003, 75928] |
[1] |
1 |
[57, 1003, 75928] |
100 |
C2 x C50 |
27) |
[57, 811, 132952] |
[1] |
1 |
[57, 811, 132952] |
100 |
C2 x C50 |
28) |
[57, 193, 1774] |
[1] |
1 |
[57, 193, 1774] |
100 |
C2 x C50 |
29) |
[57, 715, 93592] |
[1] |
1 |
[57, 715, 93592] |
100 |
C2 x C50 |
30) |
[57, 277, 14038] |
[1] |
1 |
[57, 277, 14038] |
100 |
C10 x C10 |
31) |
[205, 153, 5801] |
[1] |
1 |
[205, 153, 5801] |
200 |
C10 x C20 |
32) |
[209, 915, 112696] |
[1] |
1 |
[209, 915, 112696] |
100 |
C2 x C50 |
33) |
[209, 1575, 592516] |
[1] |
1 |
[209, 1575, 592516] |
100 |
C2 x C50 |
34) |
[76, 102, 2297] |
[2, 2] |
1 |
[76, 102, 2297] |
50 |
C50 |
35) |
[8, 1718, 727513] |
[1] |
1 |
[8, 1718, 727513] |
100 |
C2 x C50 |
36) |
[8, 1842, 848041] |
[1] |
1 |
[8, 1842, 848041] |
100 |
C100 |
37) |
[8, 1458, 530473] |
[1] |
1 |
[8, 1458, 530473] |
100 |
C100 |
38) |
[8, 1558, 571993] |
[1] |
1 |
[8, 1558, 571993] |
100 |
C100 |
39) |
[8, 1222, 290089] |
[1] |
1 |
[8, 1222, 290089] |
100 |
C100 |
40) |
[5, 1277, 340981] |
[1] |
1 |
[5, 1277, 340981] |
100 |
C100 |
41) |
[5, 1686, 694969] |
[1] |
1 |
[5, 1686, 694969] |
100 |
C100 |
42) |
[5, 1286, 401929] |
[1] |
1 |
[5, 1286, 401929] |
100 |
C2 x C50 |
43) |
[5, 1597, 608341] |
[1] |
1 |
[5, 1597, 608341] |
100 |
C100 |
44) |
[5, 1654, 665929] |
[1] |
1 |
[5, 1654, 665929] |
100 |
C100 |
45) |
[5, 1717, 732061] |
[1] |
1 |
[5, 1717, 732061] |
100 |
C2 x C50 |
46) |
[5, 1686, 708649] |
[1] |
1 |
[5, 1686, 708649] |
100 |
C100 |
47) |
[5, 1517, 552541] |
[1] |
1 |
[5, 1517, 552541] |
100 |
C100 |
48) |
[29, 1037, 71461] |
[1] |
1 |
[29, 1037, 71461] |
100 |
C2 x C50 |
49) |
[92, 1138, 161473] |
[1] |
1 |
[92, 1138, 161473] |
100 |
C100 |
50) |
[124, 162, 4577] |
[1] |
1 |
[124, 162, 4577] |
100 |
C2 x C50 |
51) |
[3605, 141, 4069] |
[1] |
1 |
[3605, 141, 4069] |
200 |
C2 x C100 |
52) |
[24, 1510, 569161] |
[1] |
1 |
[24, 1510, 569161] |
100 |
C100 |
53) |
[24, 190, 8161] |
[2, 2] |
1 |
[24, 190, 8161] |
50 |
C50 |
54) |
[24, 430, 45841] |
[1] |
1 |
[24, 430, 45841] |
100 |
C5 x C20 |
55) |
[24, 1114, 232273] |
[1] |
1 |
[24, 1114, 232273] |
100 |
C10 x C10 |
56) |
[24, 1270, 298681] |
[1] |
1 |
[24, 1270, 298681] |
100 |
C100 |
57) |
[24, 1174, 198553] |
[1] |
1 |
[24, 1174, 198553] |
100 |
C5 x C20 |
58) |
[24, 1126, 278569] |
[1] |
1 |
[24, 1126, 278569] |
100 |
C2 x C50 |
59) |
[24, 286, 18913] |
[1] |
1 |
[24, 286, 18913] |
100 |
C100 |
60) |
[24, 1306, 325009] |
[1] |
1 |
[24, 1306, 325009] |
100 |
C100 |
61) |
[24, 1114, 167953] |
[1] |
1 |
[24, 1114, 167953] |
100 |
C100 |
62) |
[24, 874, 95713] |
[1] |
1 |
[24, 874, 95713] |
100 |
C100 |
63) |
[2905, 487, 52756] |
[1] |
1 |
[2905, 487, 52756] |
200 |
C2 x C100 |
64) |
[105, 1279, 376804] |
[1] |
1 |
[105, 1279, 376804] |
200 |
C2 x C100 |
65) |
[105, 1006, 170689] |
[1] |
1 |
[105, 1006, 170689] |
200 |
C2 x C2 x C50 |
66) |
[105, 691, 56344] |
[1] |
1 |
[105, 691, 56344] |
200 |
C2 x C100 |
67) |
[764, 398, 12097] |
[1] |
1 |
[764, 398, 12097] |
100 |
C100 |
68) |
[141, 202, 9637] |
[1] |
1 |
[141, 202, 9637] |
100 |
C2 x C50 |
69) |
[141, 173, 6601] |
[1] |
1 |
[141, 173, 6601] |
100 |
C2 x C50 |
70) |
[152, 174, 5137] |
[1] |
1 |
[152, 174, 5137] |
100 |
C100 |
71) |
[152, 1018, 93553] |
[1] |
1 |
[152, 1018, 93553] |
100 |
C100 |
72) |
[40, 256, 7384] |
[1] |
1 |
[40, 256, 7384] |
200 |
C2 x C100 |
73) |
[140, 774, 93769] |
[1] |
1 |
[140, 774, 93769] |
200 |
C2 x C100 |
74) |
[140, 942, 19681] |
[1] |
1 |
[140, 942, 19681] |
200 |
C2 x C100 |
75) |
[140, 806, 142249] |
[1] |
1 |
[140, 806, 142249] |
200 |
C2 x C2 x C50 |
76) |
[113, 242, 10573] |
[1] |
1 |
[113, 242, 10573] |
100 |
C100 |
77) |
[113, 317, 18766] |
[1] |
1 |
[113, 317, 18766] |
100 |
C2 x C50 |
78) |
[248, 998, 25801] |
[1] |
1 |
[248, 998, 25801] |
100 |
C100 |
79) |
[185, 249, 2134] |
[1] |
1 |
[185, 249, 2134] |
200 |
C2 x C100 |
80) |
[185, 747, 37336] |
[1] |
1 |
[185, 747, 37336] |
200 |
C2 x C100 |
81) |
[185, 1111, 308164] |
[1] |
1 |
[185, 1111, 308164] |
200 |
C200 |
82) |
[89, 819, 153784] |
[1] |
1 |
[89, 819, 153784] |
100 |
C2 x C50 |
83) |
[89, 831, 172084] |
[1] |
1 |
[89, 831, 172084] |
100 |
C100 |
84) |
[89, 1566, 577489] |
[1] |
1 |
[89, 1566, 577489] |
100 |
C10 x C10 |
85) |
[53, 993, 222013] |
[1] |
1 |
[53, 993, 222013] |
100 |
C100 |
86) |
[329, 1086, 163249] |
[1] |
1 |
[329, 1086, 163249] |
100 |
C100 |
87) |
[329, 451, 32344] |
[1] |
1 |
[329, 451, 32344] |
100 |
C2 x C50 |
88) |
[329, 855, 30676] |
[1] |
1 |
[329, 855, 30676] |
100 |
C100 |
89) |
[3160, 346, 1489] |
[1] |
1 |
[3160, 346, 1489] |
200 |
C2 x C100 |
90) |
[281, 619, 19288] |
[1] |
1 |
[281, 619, 19288] |
100 |
C100 |
91) |
[184, 162, 6377] |
[1] |
1 |
[184, 162, 6377] |
100 |
C2 x C50 |
92) |
[177, 526, 66337] |
[1] |
1 |
[177, 526, 66337] |
100 |
C100 |
93) |
[28, 778, 135193] |
[1] |
1 |
[28, 778, 135193] |
100 |
C5 x C20 |
94) |
[1677, 1045, 222277] |
[1] |
1 |
[1677, 1045, 222277] |
400 |
C2 x C200 |
95) |
[33, 325, 24022] |
[1] |
1 |
[33, 325, 24022] |
100 |
C2 x C50 |
96) |
[33, 991, 128692] |
[1] |
1 |
[33, 991, 128692] |
100 |
C100 |
97) |
[33, 1078, 237721] |
[1] |
1 |
[33, 1078, 237721] |
100 |
C2 x C50 |
98) |
[33, 1519, 571684] |
[1] |
1 |
[33, 1519, 571684] |
100 |
C10 x C10 |
99) |
[33, 1222, 297289] |
[1] |
1 |
[33, 1222, 297289] |
100 |
C100 |
100) |
[33, 861, 184662] |
[1] |
1 |
[33, 861, 184662] |
100 |
C10 x C10 |
101) |
[33, 1366, 432697] |
[1] |
1 |
[33, 1366, 432697] |
100 |
C2 x C50 |
102) |
[33, 925, 25798] |
[1] |
1 |
[33, 925, 25798] |
100 |
C2 x C50 |
103) |
[492, 898, 4801] |
[1] |
1 |
[492, 898, 4801] |
200 |
C2 x C100 |
104) |
[2924, 450, 3841] |
[1] |
1 |
[2924, 450, 3841] |
400 |
C2 x C200 |
105) |
[1461, 1189, 335533] |
[1] |
1 |
[1461, 1189, 335533] |
100 |
C2 x C50 |
106) |
[17, 297, 20518] |
[1] |
1 |
[17, 297, 20518] |
100 |
C100 |
107) |
[17, 1231, 361972] |
[1] |
1 |
[17, 1231, 361972] |
100 |
C5 x C20 |
108) |
[17, 1622, 647929] |
[1] |
1 |
[17, 1622, 647929] |
100 |
C100 |
109) |
[17, 1571, 613912] |
[1] |
1 |
[17, 1571, 613912] |
100 |
C2 x C50 |
110) |
[17, 1387, 444184] |
[1] |
1 |
[17, 1387, 444184] |
100 |
C2 x C50 |
111) |
[17, 249, 10294] |
[1] |
1 |
[17, 249, 10294] |
100 |
C100 |
112) |
[17, 1603, 622168] |
[1] |
1 |
[17, 1603, 622168] |
100 |
C10 x C10 |
113) |
[17, 1243, 377656] |
[1] |
1 |
[17, 1243, 377656] |
100 |
C100 |
114) |
[264, 706, 65209] |
[1] |
1 |
[264, 706, 65209] |
200 |
C10 x C20 |
115) |
[2801, 519, 33028] |
[1] |
1 |
[2801, 519, 33028] |
100 |
C100 |
116) |
[3473, 203, 2488] |
[1] |
1 |
[3473, 203, 2488] |
100 |
C5 x C20 |
117) |
[133, 189, 8897] |
[1] |
1 |
[133, 189, 8897] |
100 |
C2 x C50 |
118) |
[668, 558, 11041] |
[1] |
1 |
[668, 558, 11041] |
100 |
C5 x C20 |
119) |
[77, 822, 19849] |
[1] |
1 |
[77, 822, 19849] |
100 |
C5 x C20 |
120) |
[393, 175, 6772] |
[1] |
1 |
[393, 175, 6772] |
100 |
C100 |
121) |
[701, 981, 25909] |
[1] |
1 |
[701, 981, 25909] |
100 |
C100 |
122) |
[188, 154, 5177] |
[1] |
1 |
[188, 154, 5177] |
100 |
C2 x C50 |
123) |
[188, 898, 32401] |
[1] |
1 |
[188, 898, 32401] |
100 |
C100 |
124) |
[1145, 1007, 44836] |
[1] |
1 |
[1145, 1007, 44836] |
400 |
C2 x C200 |
125) |
[44, 1150, 329041] |
[1] |
1 |
[44, 1150, 329041] |
100 |
C100 |
126) |
[44, 1194, 246409] |
[1] |
1 |
[44, 1194, 246409] |
100 |
C2 x C50 |
127) |
[44, 1410, 485761] |
[1] |
1 |
[44, 1410, 485761] |
100 |
C2 x C50 |
128) |
[12, 1198, 341473] |
[1] |
1 |
[12, 1198, 341473] |
100 |
C2 x C50 |
129) |
[12, 922, 160249] |
[1] |
1 |
[12, 922, 160249] |
100 |
C10 x C10 |
130) |
[12, 334, 24817] |
[1] |
1 |
[12, 334, 24817] |
100 |
C2 x C50 |
131) |
[12, 1522, 541489] |
[1] |
1 |
[12, 1522, 541489] |
100 |
C10 x C10 |
132) |
[12, 1330, 380017] |
[1] |
1 |
[12, 1330, 380017] |
100 |
C2 x C50 |
133) |
[12, 1258, 298441] |
[1] |
1 |
[12, 1258, 298441] |
100 |
C2 x C50 |
134) |
[12, 1186, 328417] |
[1] |
1 |
[12, 1186, 328417] |
100 |
C2 x C50 |
135) |
[12, 1402, 432601] |
[1] |
1 |
[12, 1402, 432601] |
100 |
C10 x C10 |
136) |
[12, 382, 35713] |
[1] |
1 |
[12, 382, 35713] |
100 |
C2 x C50 |
137) |
[12, 1426, 505297] |
[1] |
1 |
[12, 1426, 505297] |
100 |
C2 x C50 |
138) |
[1545, 757, 96526] |
[1] |
1 |
[1545, 757, 96526] |
200 |
C2 x C100 |
139) |
[21, 1054, 84193] |
[1] |
1 |
[21, 1054, 84193] |
100 |
C2 x C50 |
140) |
[21, 1369, 386509] |
[1] |
1 |
[21, 1369, 386509] |
100 |
C2 x C50 |
141) |
[21, 886, 187849] |
[1] |
1 |
[21, 886, 187849] |
100 |
C2 x C50 |
142) |
[21, 1345, 408781] |
[1] |
1 |
[21, 1345, 408781] |
100 |
C2 x C50 |
143) |
[2417, 651, 3832] |
[1] |
1 |
[2417, 651, 3832] |
100 |
C100 |
144) |
[56, 296, 17368] |
[1] |
1 |
[56, 296, 17368] |
100 |
C2 x C50 |
145) |
[56, 302, 14737] |
[1] |
1 |
[56, 302, 14737] |
100 |
C100 |
146) |
[485, 645, 28225] |
[1] |
1 |
[485, 645, 28225] |
200 |
C200 |
147) |
[41, 899, 161368] |
[1] |
1 |
[41, 899, 161368] |
100 |
C2 x C50 |
148) |
[41, 827, 57976] |
[1] |
1 |
[41, 827, 57976] |
100 |
C100 |
149) |
[41, 461, 53038] |
[1] |
1 |
[41, 461, 53038] |
100 |
C2 x C50 |
150) |
[41, 939, 219928] |
[1] |
1 |
[41, 939, 219928] |
100 |
C2 x C50 |
151) |
[41, 1447, 465796] |
[1] |
1 |
[41, 1447, 465796] |
100 |
C2 x C50 |
152) |
[41, 241, 3358] |
[1] |
1 |
[41, 241, 3358] |
100 |
C2 x C50 |
153) |
[397, 157, 5269] |
[1] |
1 |
[397, 157, 5269] |
100 |
C100 |
154) |
[633, 157, 2206] |
[1] |
1 |
[633, 157, 2206] |
100 |
C2 x C50 |
155) |
[101, 669, 96109] |
[1] |
1 |
[101, 669, 96109] |
100 |
C100 |
156) |
[2345, 687, 18916] |
[1] |
1 |
[2345, 687, 18916] |
200 |
C2 x C100 |
157) |
[69, 1021, 70429] |
[1] |
1 |
[69, 1021, 70429] |
100 |
C100 |
158) |
[65, 1406, 484849] |
[1] |
1 |
[65, 1406, 484849] |
200 |
C2 x C2 x C50 |
159) |
[65, 1911, 912964] |
[1] |
1 |
[65, 1911, 912964] |
200 |
C2 x C100 |
160) |
[65, 1299, 401944] |
[1] |
1 |
[65, 1299, 401944] |
200 |
C2 x C100 |
161) |
[65, 1171, 202264] |
[1] |
1 |
[65, 1171, 202264] |
200 |
C2 x C100 |