Genus 2 Curves Database Igusa CM Invariants Database Quartic CM Fields Database

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]

[2][4][6][8][10][12][14][16][18][20][22][24][26][28][30][32][34][36][38][40][42][44][46][48]
[50][52][54][56][58][60][62][64][66][68][70][72][74][76][78][80][82][84][86][88][90][92][94][96]
[98][100][102][104][106][108][110][112][114][116][118][120][122][124][126][128][130][132][134][136][138][140][142][144]
[146][148][150][152][154][156][158][160][162][164][166][168][170][172][174][176][178][180][182][184][186][188][190][192]
[194][196][198][200][202][204][206][208][210][212][214][216][218][220][222][224][226][228][230][232][234][236][238][240]
[242][244][246][248][250][252][254][256][258][260][262][264][266][268][270][272][274][276][278][280][282][284][286][288]
[290][292][294][296][298][300][302][304][306][308][310][312][314][316][318][320][322][324][326][328][330][332][334][336]
[338][340][342][344][346][348][350][352][354][356][358][360][362][364][366][368][370][372][374][376][378][380][382][384]
[386][388][390][392][394][396][398][400][402][404][406][408][410][412][414][416][418][420][422][424][426][428][430][432]
[434][436][438][440][442][444][446][448][450][452][454][456][458][460][462][464][466][468][470][472][474][476][478][480]
[482][484][486][488][490][492][494][496][498][500][502][504][506][508][510][512][514][516][518][520][522][524][526][528]
[530][532][534][536][538][540][542][544][546][548][550][552][554][556][558][560][562][564][566][568][570][572][574][576]
[578][580][582][584][586][588][590][592][594][596][598][600][602][604][606][608][610][612][614][616][618][620][622][624]
[626][628][630][632][634][636][638][640][642][644][646][648][650][652][654][656][658][660][662][664][666][668][670][672]
[674][676][678][680][682][684][686][688][690][692][694][696][698][700][702][704][706][708][710][712][714][716][718][720]
[722][724][726][728][730][732][734][736][738][740][742][744][746][748][750][752][754][756][758][760][762][764][766][768]
[770][772][774][776][778][780][782][784][786][788][790][792][794][796][798][800][802][804][806][808][810][812][814][816]
[818][820][822][824][826][828][830][832][834][836][838][840][842][844][846][848][850][852][854][856][858][860][862][864]
[1106][1108][1110][1112][1114][1116][1118][1120][1122][1124][1126][1128][1130][1132][1134][1136][1138][1140][1142][1144][1146][1148][1150][1152]

Degree 90 Igusa CM invariants of non-normal (D4) fields: 89

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 97, 2273] [1] 1 [317, 97, 2273] 45 C3 x C15
2) [157, 173, 7129] [1] 1 [157, 173, 7129] 45 C45
3) [157, 153, 3929] [1] 1 [157, 153, 3929] 45 C45
4) [229, 137, 4177] [1] 1 [229, 137, 4177] 135 C3 x C45
5) [1049, 870, 122089] [1] 1 [1049, 870, 122089] 45 C3 x C15
6) [109, 250, 11701] [1] 1 [109, 250, 11701] 45 C45
7) [733, 222, 593] [1] 1 [733, 222, 593] 135 C3 x C45
8) [13, 1790, 379825] [1] 2 [13, 1790, 379825] 90 C90
9) [13, 809, 142297] [1] 1 [13, 809, 142297] 45 C45
10) [13, 457, 16381] [1] 1 [13, 457, 16381] 45 C45
11) [13, 653, 91129] [1] 1 [13, 653, 91129] 45 C45
12) [8, 1042, 269641] [1] 1 [8, 1042, 269641] 45 C45
13) [8, 1158, 289033] [1] 1 [8, 1158, 289033] 45 C45
14) [8, 394, 37657] [1] 2 [8, 394, 37657] 90 C90
15) [8, 350, 26017] [1] 1 [8, 350, 26017] 45 C45
16) [8, 666, 95401] [1] 2 [8, 666, 95401] 90 C90
17) [8, 822, 101209] [1] 1 [8, 822, 101209] 45 C45
18) [8, 858, 182473] [1] 2 [8, 858, 182473] 90 C3 x C30
19) [8, 1350, 369097] [1] 1 [8, 1350, 369097] 45 C45
20) [8, 882, 190249] [1] 1 [8, 882, 190249] 45 C45
21) [8, 794, 155017] [1] 2 [8, 794, 155017] 90 C90
22) [8, 814, 121841] [1] 2 [8, 814, 121841] 90 C90
23) [8, 1238, 267961] [1] 1 [8, 1238, 267961] 45 C45
24) [5, 1141, 302009] [1] 1 [5, 1141, 302009] 45 C45
25) [5, 613, 92041] [1] 1 [5, 613, 92041] 45 C45
26) [5, 717, 117241] [1] 1 [5, 717, 117241] 45 C45
27) [5, 833, 145721] [1] 1 [5, 833, 145721] 45 C45
28) [5, 673, 111521] [1] 1 [5, 673, 111521] 45 C45
29) [5, 966, 225289] [1] 1 [5, 966, 225289] 45 C45
30) [5, 829, 160049] [1] 1 [5, 829, 160049] 45 C45
31) [5, 1021, 222329] [1] 1 [5, 1021, 222329] 45 C45
32) [5, 437, 47681] [1] 1 [5, 437, 47681] 45 C45
33) [5, 654, 91249] [1] 1 [5, 654, 91249] 45 C45
34) [5, 1026, 226189] [1] 1 [5, 1026, 226189] 45 C45
35) [5, 797, 138641] [1] 1 [5, 797, 138641] 45 C45
36) [5, 238, 14081] [2, 2] 1 [5, 238, 14081] 15 C15
37) [5, 1194, 300229] [1] 1 [5, 1194, 300229] 45 C45
38) [5, 817, 139861] [1] 1 [5, 817, 139861] 45 C45
39) [5, 1221, 363249] [1] 2 [5, 1221, 363249] 90 C90
40) [5, 569, 80929] [1] 1 [5, 569, 80929] 45 C45
41) [5, 158, 5521] [2, 2] 1 [5, 158, 5521] 15 C15
42) [5, 1689, 702369] [1] 2 [5, 1689, 702369] 90 C90
43) [5, 1001, 213949] [1] 1 [5, 1001, 213949] 45 C45
44) [5, 263, 16741] [1] 2 [5, 263, 16741] 90 C90
45) [5, 439, 47629] [1] 2 [5, 439, 47629] 90 C90
46) [5, 479, 57349] [1] 2 [5, 479, 57349] 90 C3 x C30
47) [5, 886, 164249] [1] 1 [5, 886, 164249] 45 C45
48) [5, 578, 81901] [1] 1 [5, 578, 81901] 45 C3 x C15
49) [5, 214, 11369] [2, 2] 1 [5, 214, 11369] 15 C15
50) [29, 236, 9748] [1] 2 [29, 236, 9748] 90 C90
51) [29, 477, 24337] [1] 1 [29, 477, 24337] 45 C45
52) [149, 141, 4933] [1] 1 [149, 141, 4933] 45 C45
53) [149, 186, 8053] [1] 1 [149, 186, 8053] 45 C45
54) [149, 180, 5716] [1] 2 [149, 180, 5716] 90 C90
55) [1877, 825, 757] [1] 1 [1877, 825, 757] 45 C45
56) [113, 918, 29881] [1] 1 [113, 918, 29881] 45 C45
57) [89, 807, 135556] [1] 1 [89, 807, 135556] 45 C45
58) [281, 791, 14164] [1] 1 [281, 791, 14164] 45 C45
59) [37, 174, 6977] [1] 1 [37, 174, 6977] 45 C45
60) [37, 150, 3257] [2, 2] 1 [37, 150, 3257] 15 C15
61) [37, 862, 156753] [1] 1 [37, 862, 156753] 45 C45
62) [5573, 141, 3577] [1] 1 [5573, 141, 3577] 45 C45
63) [61, 130, 2029] [1] 1 [61, 130, 2029] 45 C45
64) [197, 157, 6113] [1] 1 [197, 157, 6113] 45 C45
65) [17, 354, 27997] [1] 1 [17, 354, 27997] 45 C45
66) [17, 1086, 196657] [1] 1 [17, 1086, 196657] 45 C45
67) [17, 118, 3209] [1] 1 [17, 118, 3209] 45 C45
68) [17, 718, 126433] [1] 1 [17, 718, 126433] 45 C45
69) [17, 118, 3209] [2, 2] 1 [17, 118, 3209] 45 C45
70) [17, 1238, 295033] [1] 1 [17, 1238, 295033] 45 C45
71) [17, 1527, 582724] [1] 1 [17, 1527, 582724] 45 C45
72) [17, 1230, 299617] [1] 1 [17, 1230, 299617] 45 C3 x C15
73) [17, 1647, 660196] [1] 1 [17, 1647, 660196] 45 C45
74) [173, 145, 3137] [1] 1 [173, 145, 3137] 45 C45
75) [173, 222, 1249] [1] 1 [173, 222, 1249] 45 C45
76) [173, 789, 5077] [1] 1 [173, 789, 5077] 45 C3 x C15
77) [2909, 477, 38701] [1] 1 [2909, 477, 38701] 45 C45
78) [3041, 399, 2548] [1] 2 [3041, 399, 2548] 90 C90
79) [1013, 850, 144157] [1] 1 [1013, 850, 144157] 45 C45
80) [569, 394, 18325] [1] 1 [569, 394, 18325] 45 C45
81) [569, 975, 42916] [1] 1 [569, 975, 42916] 45 C45
82) [44, 380, 34516] [1] 2 [44, 380, 34516] 90 C90
83) [1004, 786, 129349] [1] 2 [1004, 786, 129349] 90 C3 x C30
84) [41, 1038, 79777] [1] 1 [41, 1038, 79777] 45 C45
85) [41, 1431, 511684] [1] 1 [41, 1431, 511684] 45 C3 x C15
86) [41, 1311, 417124] [1] 1 [41, 1311, 417124] 45 C45
87) [41, 1735, 748036] [1] 1 [41, 1735, 748036] 45 C45
88) [829, 497, 51597] [1] 2 [829, 497, 51597] 90 C90
89) [2633, 567, 724] [1] 1 [2633, 567, 724] 45 C45