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 208 Igusa CM invariants of non-normal (D4) fields: 37

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [1717, 1173, 219929] [1] 1 [1717, 1173, 219929] 208 C2 x C104
2) [317, 597, 54153] [1] 2 [317, 597, 54153] 208 C2 x C104
3) [661, 1717, 736857] [1] 1 [661, 1717, 736857] 104 C104
4) [236, 402, 25297] [1] 1 [236, 402, 25297] 104 C2 x C52
5) [88, 250, 14833] [1] 1 [88, 250, 14833] 104 C2 x C52
6) [97, 886, 8457] [1] 1 [97, 886, 8457] 104 C104
7) [985, 151, 3484] [1] 1 [985, 151, 3484] 624 C4 x C156
8) [913, 187, 6688] [1] 1 [913, 187, 6688] 104 C2 x C52
9) [517, 1089, 280841] [1] 1 [517, 1089, 280841] 104 C2 x C52
10) [13, 115, 3043] [1] 1 [13, 115, 3043] 104 C2 x C52
11) [5, 837, 165241] [1] 1 [5, 837, 165241] 104 C104
12) [5, 1481, 536089] [1] 1 [5, 1481, 536089] 104 C104
13) [5, 1721, 723929] [1] 1 [5, 1721, 723929] 104 C104
14) [5, 1766, 771689] [1] 1 [5, 1766, 771689] 104 C104
15) [29, 582, 84217] [1] 1 [29, 582, 84217] 104 C2 x C52
16) [92, 570, 79753] [1] 1 [92, 570, 79753] 104 C104
17) [2501, 713, 21425] [1] 1 [2501, 713, 21425] 416 C2 x C208
18) [1093, 1237, 237993] [1] 1 [1093, 1237, 237993] 520 C520
19) [1453, 1309, 419289] [1] 1 [1453, 1309, 419289] 104 C104
20) [248, 474, 49969] [1] 1 [248, 474, 49969] 104 C104
21) [248, 426, 33217] [1] 1 [248, 426, 33217] 104 C104
22) [185, 551, 75484] [1] 1 [185, 551, 75484] 208 C4 x C52
23) [305, 483, 56416] [1] 1 [305, 483, 56416] 208 C4 x C52
24) [28, 574, 81361] [1] 1 [28, 574, 81361] 104 C2 x C52
25) [197, 437, 36661] [1] 1 [197, 437, 36661] 104 C104
26) [965, 161, 4309] [1] 1 [965, 161, 4309] 208 C2 x C2 x C52
27) [1061, 117, 3157] [1] 1 [1061, 117, 3157] 104 C2 x C52
28) [668, 282, 9193] [1] 1 [668, 282, 9193] 104 C104
29) [77, 497, 57421] [1] 1 [77, 497, 57421] 104 C2 x C52
30) [653, 309, 19789] [1] 1 [653, 309, 19789] 104 C2 x C52
31) [73, 662, 14953] [1] 1 [73, 662, 14953] 104 C104
32) [73, 155, 5988] [1] 1 [73, 155, 5988] 104 C104
33) [73, 319, 25276] [1] 1 [73, 319, 25276] 104 C2 x C52
34) [73, 667, 34116] [1] 1 [73, 667, 34116] 104 C104
35) [101, 537, 69037] [1] 1 [101, 537, 69037] 104 C2 x C52
36) [101, 417, 34357] [1] 1 [101, 417, 34357] 104 C2 x C52
37) [1949, 1033, 227305] [1] 1 [1949, 1033, 227305] 104 C104