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 272 Igusa CM invariants of non-normal (D4) fields: 30

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [237, 385, 19933] [1] 1 [237, 385, 19933] 136 C136
2) [104, 578, 82585] [1] 1 [104, 578, 82585] 272 C4 x C68
3) [109, 358, 16345] [1] 1 [109, 358, 16345] 136 C2 x C68
4) [797, 245, 13213] [1] 1 [797, 245, 13213] 136 C136
5) [733, 1069, 61209] [1] 1 [733, 1069, 61209] 408 C408
6) [377, 399, 28396] [1] 1 [377, 399, 28396] 272 C4 x C68
7) [13, 550, 73753] [1] 1 [13, 550, 73753] 136 C136
8) [5, 1673, 680201] [1] 1 [5, 1673, 680201] 136 C136
9) [5, 1313, 355961] [1] 1 [5, 1313, 355961] 136 C136
10) [5, 1313, 421961] [1] 1 [5, 1313, 421961] 136 C136
11) [29, 1021, 245929] [1] 1 [29, 1021, 245929] 136 C136
12) [29, 1117, 155257] [1] 1 [29, 1117, 155257] 136 C136
13) [428, 426, 43657] [1] 1 [428, 426, 43657] 136 C136
14) [40, 418, 34681] [1] 1 [40, 418, 34681] 272 C2 x C2 x C68
15) [509, 998, 216425] [1] 1 [509, 998, 216425] 136 C136
16) [89, 251, 14660] [1] 1 [89, 251, 14660] 136 C136
17) [341, 417, 33157] [1] 1 [341, 417, 33157] 136 C136
18) [37, 1661, 653017] [1] 1 [37, 1661, 653017] 136 C136
19) [293, 441, 39757] [1] 1 [293, 441, 39757] 136 C136
20) [508, 322, 7633] [1] 1 [508, 322, 7633] 136 C2 x C68
21) [17, 662, 63593] [1] 1 [17, 662, 63593] 136 C136
22) [453, 337, 9253] [1] 1 [453, 337, 9253] 136 C136
23) [773, 249, 10669] [1] 1 [773, 249, 10669] 136 C136
24) [188, 546, 73777] [1] 1 [188, 546, 73777] 136 C2 x C68
25) [653, 317, 23653] [1] 1 [653, 317, 23653] 136 C2 x C68
26) [337, 367, 14716] [1] 1 [337, 367, 14716] 136 C2 x C68
27) [632, 330, 26593] [1] 1 [632, 330, 26593] 136 C2 x C68
28) [673, 307, 22048] [1] 1 [673, 307, 22048] 136 C2 x C68
29) [73, 1222, 231993] [1] 1 [73, 1222, 231993] 136 C136
30) [233, 447, 40108] [1] 1 [233, 447, 40108] 136 C2 x C68