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 260 Igusa CM invariants of non-normal (D4) fields: 46

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [137, 357, 27718] [1] 1 [137, 357, 27718] 130 C130
2) [137, 830, 152497] [1] 1 [137, 830, 152497] 130 C130
3) [129, 226, 12253] [1] 1 [129, 226, 12253] 130 C130
4) [104, 1286, 319849] [1] 1 [104, 1286, 319849] 260 C2 x C130
5) [641, 165, 6646] [1] 1 [641, 165, 6646] 130 C130
6) [57, 1687, 711364] [1] 1 [57, 1687, 711364] 130 C130
7) [377, 915, 50872] [1] 1 [377, 915, 50872] 260 C260
8) [8, 1830, 835657] [1] 1 [8, 1830, 835657] 130 C130
9) [8, 1670, 692617] [1] 1 [8, 1670, 692617] 130 C130
10) [5, 1766, 776809] [1] 1 [5, 1766, 776809] 130 C130
11) [5, 1102, 277681] [1] 1 [5, 1102, 277681] 130 C130
12) [29, 1149, 270013] [1] 1 [29, 1149, 270013] 130 C130
13) [29, 1569, 610909] [1] 1 [29, 1569, 610909] 130 C130
14) [92, 746, 86137] [1] 1 [92, 746, 86137] 130 C130
15) [1685, 881, 8269] [1] 1 [1685, 881, 8269] 260 C2 x C130
16) [221, 990, 18721] [1] 1 [221, 990, 18721] 260 C260
17) [2489, 639, 26788] [1] 1 [2489, 639, 26788] 130 C130
18) [152, 726, 129337] [1] 1 [152, 726, 129337] 130 C130
19) [149, 765, 64021] [1] 1 [149, 765, 64021] 130 C130
20) [149, 945, 154381] [1] 1 [149, 945, 154381] 130 C130
21) [509, 929, 22213] [1] 1 [509, 929, 22213] 130 C130
22) [53, 1077, 267709] [1] 1 [53, 1077, 267709] 130 C130
23) [329, 1359, 392548] [1] 1 [329, 1359, 392548] 130 C130
24) [17, 1687, 697684] [1] 1 [17, 1687, 697684] 130 C130
25) [17, 1671, 685204] [1] 1 [17, 1671, 685204] 130 C130
26) [545, 1191, 223684] [1] 1 [545, 1191, 223684] 260 C260
27) [2969, 447, 31396] [1] 1 [2969, 447, 31396] 130 C130
28) [1241, 1103, 167332] [1] 1 [1241, 1103, 167332] 260 C260
29) [668, 962, 14929] [1] 1 [668, 962, 14929] 130 C130
30) [77, 941, 182389] [1] 1 [77, 941, 182389] 130 C130
31) [77, 801, 117877] [1] 1 [77, 801, 117877] 130 C130
32) [44, 114, 3238] [1] 1 [44, 114, 3238] 130 C130
33) [2577, 631, 67972] [1] 1 [2577, 631, 67972] 130 C130
34) [12, 1666, 674689] [1] 1 [12, 1666, 674689] 130 C130
35) [12, 1846, 851737] [1] 1 [12, 1846, 851737] 130 C130
36) [12, 1138, 318961] [1] 1 [12, 1138, 318961] 130 C130
37) [21, 997, 68821] [1] 1 [21, 997, 68821] 130 C130
38) [21, 1093, 289837] [1] 1 [21, 1093, 289837] 130 C130
39) [21, 1093, 298237] [1] 1 [21, 1093, 298237] 130 C130
40) [21, 1681, 706309] [1] 1 [21, 1681, 706309] 130 C130
41) [56, 1254, 328393] [1] 1 [56, 1254, 328393] 130 C130
42) [41, 942, 97816] [1] 1 [41, 942, 97816] 130 C130
43) [201, 895, 69556] [1] 1 [201, 895, 69556] 130 C130
44) [2105, 831, 108964] [1] 1 [2105, 831, 108964] 260 C260
45) [65, 233, 6406] [1] 1 [65, 233, 6406] 260 C260
46) [65, 1526, 544729] [1] 1 [65, 1526, 544729] 260 C260