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 110 Igusa CM invariants of non-normal (D4) fields: 46

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [229, 129, 2729] [1] 1 [229, 129, 2729] 165 C165
2) [269, 121, 3593] [1] 1 [269, 121, 3593] 55 C55
3) [269, 706, 114925] [1] 1 [269, 706, 114925] 55 C55
4) [236, 270, 6661] [1] 2 [236, 270, 6661] 110 C110
5) [349, 81, 1553] [1] 1 [349, 81, 1553] 55 C55
6) [13, 193, 9049] [1] 1 [13, 193, 9049] 55 C55
7) [13, 394, 27109] [1] 1 [13, 394, 27109] 55 C55
8) [977, 738, 132253] [1] 1 [977, 738, 132253] 55 C55
9) [8, 1122, 242521] [1] 1 [8, 1122, 242521] 55 C55
10) [8, 870, 172297] [1] 1 [8, 870, 172297] 55 C55
11) [8, 790, 99577] [1] 1 [8, 790, 99577] 55 C55
12) [8, 1206, 352057] [1] 1 [8, 1206, 352057] 55 C55
13) [8, 1266, 342889] [1] 1 [8, 1266, 342889] 55 C55
14) [8, 1506, 519577] [1] 1 [8, 1506, 519577] 55 C55
15) [8, 506, 56809] [1] 2 [8, 506, 56809] 110 C110
16) [5, 1481, 531229] [1] 1 [5, 1481, 531229] 55 C55
17) [5, 1561, 572629] [1] 1 [5, 1561, 572629] 55 C55
18) [5, 929, 213229] [1] 1 [5, 929, 213229] 55 C55
19) [5, 713, 127081] [1] 1 [5, 713, 127081] 55 C55
20) [5, 1129, 271129] [1] 1 [5, 1129, 271129] 55 C55
21) [5, 1709, 716389] [1] 1 [5, 1709, 716389] 55 C55
22) [5, 1641, 673069] [1] 1 [5, 1641, 673069] 55 C55
23) [5, 1509, 530989] [1] 1 [5, 1509, 530989] 55 C55
24) [29, 271, 7333] [1] 2 [29, 271, 7333] 110 C110
25) [29, 1030, 60601] [1] 1 [29, 1030, 60601] 55 C55
26) [29, 437, 6961] [1] 1 [29, 437, 6961] 55 C55
27) [149, 669, 22453] [1] 1 [149, 669, 22453] 55 C55
28) [113, 990, 199825] [1] 2 [113, 990, 199825] 110 C110
29) [113, 878, 46273] [1] 1 [113, 878, 46273] 55 C55
30) [89, 1215, 338596] [1] 1 [89, 1215, 338596] 55 C55
31) [37, 326, 24201] [1] 1 [37, 326, 24201] 55 C55
32) [37, 237, 14033] [1] 1 [37, 237, 14033] 55 C55
33) [17, 214, 11177] [1] 1 [17, 214, 11177] 55 C55
34) [17, 1086, 288049] [1] 1 [17, 1086, 288049] 55 C55
35) [17, 214, 11177] [2, 2] 1 [17, 214, 11177] 55 C55
36) [17, 618, 30133] [1] 1 [17, 618, 30133] 55 C55
37) [17, 1022, 199921] [1] 1 [17, 1022, 199921] 55 C55
38) [1868, 706, 107797] [1] 2 [1868, 706, 107797] 110 C110
39) [181, 165, 6761] [1] 1 [181, 165, 6761] 55 C55
40) [44, 366, 31333] [1] 2 [44, 366, 31333] 110 C110
41) [73, 607, 44644] [1] 1 [73, 607, 44644] 55 C55
42) [41, 1503, 556132] [1] 1 [41, 1503, 556132] 55 C55
43) [41, 306, 15373] [1] 1 [41, 306, 15373] 55 C55
44) [41, 855, 97876] [1] 1 [41, 855, 97876] 55 C55
45) [397, 413, 6813] [1] 1 [397, 413, 6813] 55 C55
46) [101, 621, 20029] [1] 1 [101, 621, 20029] 55 C55