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 504 Igusa CM invariants of non-normal (D4) fields: 53

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [165, 857, 176641] [1] 1 [165, 857, 176641] 504 C2 x C252
2) [157, 582, 44489] [1] 1 [157, 582, 44489] 252 C252
3) [349, 537, 17561] [1] 1 [349, 537, 17561] 252 C252
4) [429, 785, 148801] [1] 1 [429, 785, 148801] 504 C2 x C2 x C126
5) [357, 701, 97057] [1] 1 [357, 701, 97057] 504 C2 x C252
6) [1544, 250, 14081] [1] 1 [1544, 250, 14081] 504 C2 x C252
7) [273, 406, 1897] [1] 1 [273, 406, 1897] 504 C2 x C252
8) [109, 825, 162281] [1] 1 [109, 825, 162281] 252 C2 x C126
9) [348, 310, 11497] [1] 1 [348, 310, 11497] 504 C2 x C2 x C126
10) [1212, 386, 17857] [1] 1 [1212, 386, 17857] 504 C2 x C252
11) [380, 262, 15641] [1] 1 [380, 262, 15641] 504 C2 x C2 x C126
12) [796, 554, 48073] [1] 1 [796, 554, 48073] 252 C252
13) [1768, 138, 2993] [1] 1 [1768, 138, 2993] 2016 C2 x C6 x C168
14) [13, 853, 175321] [1] 1 [13, 853, 175321] 252 C252
15) [556, 546, 18929] [1] 1 [556, 546, 18929] 252 C2 x C126
16) [92, 598, 44873] [1] 1 [92, 598, 44873] 252 C6 x C42
17) [93, 797, 150409] [1] 1 [93, 797, 150409] 252 C252
18) [221, 397, 38905] [1] 1 [221, 397, 38905] 504 C2 x C252
19) [1464, 290, 19561] [1] 1 [1464, 290, 19561] 504 C2 x C252
20) [428, 266, 10841] [1] 1 [428, 266, 10841] 252 C252
21) [141, 589, 61033] [1] 1 [141, 589, 61033] 252 C252
22) [40, 846, 171089] [1] 1 [40, 846, 171089] 504 C2 x C2 x C126
23) [40, 842, 174001] [1] 1 [40, 842, 174001] 504 C2 x C2 x C126
24) [140, 562, 51521] [1] 1 [140, 562, 51521] 504 C2 x C6 x C42
25) [248, 562, 37049] [1] 1 [248, 562, 37049] 252 C252
26) [1068, 418, 5233] [1] 1 [1068, 418, 5233] 504 C2 x C2 x C126
27) [332, 314, 19337] [1] 1 [332, 314, 19337] 252 C3 x C84
28) [1688, 178, 6233] [1] 1 [1688, 178, 6233] 252 C2 x C126
29) [293, 613, 55193] [1] 1 [293, 613, 55193] 252 C252
30) [28, 870, 183737] [1] 1 [28, 870, 183737] 252 C2 x C126
31) [28, 882, 192689] [1] 1 [28, 882, 192689] 252 C2 x C126
32) [445, 621, 56249] [1] 1 [445, 621, 56249] 1008 C4 x C252
33) [316, 390, 36761] [1] 1 [316, 390, 36761] 756 C3 x C252
34) [597, 581, 41257] [1] 1 [597, 581, 41257] 252 C252
35) [597, 641, 77497] [1] 1 [597, 641, 77497] 252 C3 x C84
36) [492, 578, 34321] [1] 1 [492, 578, 34321] 504 C6 x C84
37) [453, 653, 73873] [1] 1 [453, 653, 73873] 252 C252
38) [645, 641, 83209] [1] 1 [645, 641, 83209] 504 C2 x C252
39) [232, 746, 120337] [1] 1 [232, 746, 120337] 504 C2 x C2 x C126
40) [77, 925, 211577] [1] 1 [77, 925, 211577] 252 C252
41) [701, 529, 19313] [1] 1 [701, 529, 19313] 252 C2 x C126
42) [21, 838, 172537] [1] 1 [21, 838, 172537] 252 C2 x C126
43) [85, 969, 234209] [1] 1 [85, 969, 234209] 504 C2 x C252
44) [277, 573, 38801] [1] 1 [277, 573, 38801] 252 C2 x C126
45) [56, 898, 198857] [1] 1 [56, 898, 198857] 252 C2 x C126
46) [41, 598, 57257] [1] 1 [41, 598, 57257] 252 C252
47) [41, 398, 36977] [1] 1 [41, 398, 36977] 252 C252
48) [172, 662, 103369] [1] 1 [172, 662, 103369] 252 C2 x C126
49) [557, 229, 11857] [1] 1 [557, 229, 11857] 252 C252
50) [717, 581, 54097] [1] 1 [717, 581, 54097] 252 C6 x C42
51) [69, 814, 155713] [1] 1 [69, 814, 155713] 252 C252
52) [989, 469, 25073] [1] 1 [989, 469, 25073] 252 C252
53) [65, 374, 33929] [1] 1 [65, 374, 33929] 504 C2 x C252