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 312 Igusa CM invariants of non-normal (D4) fields: 24

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 405, 27613] [1] 1 [317, 405, 27613] 156 C156
2) [237, 309, 13857] [1] 1 [237, 309, 13857] 156 C2 x C78
3) [437, 293, 21353] [1] 1 [437, 293, 21353] 156 C156
4) [629, 193, 7897] [1] 1 [629, 193, 7897] 312 C2 x C2 x C78
5) [269, 501, 61069] [1] 1 [269, 501, 61069] 156 C156
6) [269, 337, 22945] [1] 1 [269, 337, 22945] 156 C2 x C78
7) [145, 214, 9129] [1] 1 [145, 214, 9129] 624 C2 x C312
8) [109, 433, 45537] [1] 1 [109, 433, 45537] 156 C2 x C78
9) [205, 397, 38121] [1] 1 [205, 397, 38121] 312 C2 x C156
10) [309, 333, 23937] [1] 1 [309, 333, 23937] 156 C2 x C78
11) [413, 265, 9193] [1] 1 [413, 265, 9193] 156 C2 x C78
12) [149, 353, 24857] [1] 1 [149, 353, 24857] 156 C2 x C78
13) [509, 257, 16385] [1] 1 [509, 257, 16385] 156 C2 x C78
14) [533, 245, 14873] [1] 1 [533, 245, 14873] 312 C2 x C2 x C78
15) [37, 517, 64741] [1] 1 [37, 517, 64741] 156 C156
16) [293, 501, 62677] [1] 1 [293, 501, 62677] 156 C156
17) [581, 221, 12065] [1] 1 [581, 221, 12065] 156 C2 x C78
18) [197, 373, 30793] [1] 1 [197, 373, 30793] 156 C2 x C78
19) [197, 549, 75301] [1] 1 [197, 549, 75301] 156 C156
20) [373, 313, 22161] [1] 1 [373, 313, 22161] 156 C2 x C78
21) [173, 385, 33553] [1] 1 [173, 385, 33553] 156 C2 x C78
22) [365, 329, 26969] [1] 1 [365, 329, 26969] 312 C2 x C2 x C78
23) [101, 597, 89077] [1] 1 [101, 597, 89077] 156 C156
24) [557, 357, 28381] [1] 1 [557, 357, 28381] 156 C156