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 308 Igusa CM invariants of non-normal (D4) fields: 32

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 941, 221017] [1] 1 [157, 941, 221017] 154 C154
2) [301, 390, 18761] [1] 1 [301, 390, 18761] 154 C154
3) [88, 626, 97177] [1] 1 [88, 626, 97177] 154 C154
4) [349, 629, 60433] [1] 1 [349, 629, 60433] 154 C154
5) [104, 506, 40609] [1] 1 [104, 506, 40609] 308 C2 x C154
6) [205, 542, 43921] [1] 1 [205, 542, 43921] 308 C308
7) [205, 809, 152089] [1] 1 [205, 809, 152089] 308 C308
8) [309, 374, 15193] [1] 1 [309, 374, 15193] 154 C154
9) [1621, 209, 7273] [1] 1 [1621, 209, 7273] 154 C154
10) [1837, 105, 2297] [1] 1 [1837, 105, 2297] 154 C154
11) [1501, 269, 14713] [1] 1 [1501, 269, 14713] 154 C154
12) [1381, 309, 6953] [1] 1 [1381, 309, 6953] 154 C154
13) [8, 782, 138769] [1] 1 [8, 782, 138769] 154 C154
14) [268, 498, 9473] [1] 1 [268, 498, 9473] 154 C154
15) [24, 914, 207673] [1] 1 [24, 914, 207673] 154 C154
16) [1685, 181, 7769] [1] 1 [1685, 181, 7769] 308 C308
17) [1781, 133, 3977] [1] 1 [1781, 133, 3977] 308 C308
18) [417, 182, 1609] [1] 1 [417, 182, 1609] 154 C154
19) [89, 310, 22601] [1] 1 [89, 310, 22601] 154 C154
20) [53, 886, 192857] [1] 1 [53, 886, 192857] 154 C154
21) [37, 918, 208313] [1] 1 [37, 918, 208313] 154 C154
22) [37, 965, 232057] [1] 1 [37, 965, 232057] 154 C154
23) [445, 761, 135769] [1] 1 [445, 761, 135769] 616 C616
24) [61, 870, 185321] [1] 1 [61, 870, 185321] 154 C154
25) [133, 953, 226753] [1] 1 [133, 953, 226753] 154 C154
26) [12, 890, 197257] [1] 1 [12, 890, 197257] 154 C154
27) [21, 694, 108313] [1] 1 [21, 694, 108313] 154 C154
28) [85, 529, 26929] [1] 1 [85, 529, 26929] 308 C308
29) [85, 654, 72929] [1] 1 [85, 654, 72929] 308 C308
30) [69, 653, 87817] [1] 1 [69, 653, 87817] 154 C154
31) [69, 878, 191617] [1] 1 [69, 878, 191617] 154 C154
32) [69, 677, 103801] [1] 1 [69, 677, 103801] 154 C154