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 2 Igusa CM invariants of non-normal (D4) fields: 64

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 25, 117] [1] 1 [157, 25, 117] 1 C1
2) [269, 17, 5] [1] 1 [269, 17, 5] 1 C1
3) [236, 32, 20] [1] 2 [236, 32, 20] 2 C2
4) [137, 35, 272] [1] 1 [137, 35, 272] 1 C1
5) [109, 17, 45] [1] 1 [109, 17, 45] 1 C1
6) [97, 94, 657] [1] 1 [97, 94, 657] 1 C1
7) [13, 29, 181] [1] 1 [13, 29, 181] 1 C1
8) [13, 41, 157] [1] 1 [13, 41, 157] 1 C1
9) [13, 9, 17] [1] 1 [13, 9, 17] 1 C1
10) [13, 18, 29] [1] 1 [13, 18, 29] 1 C1
11) [76, 18, 5] [1] 2 [76, 18, 5] 2 C2
12) [8, 50, 425] [1] 2 [8, 50, 425] 2 C2
13) [8, 66, 1017] [1] 2 [8, 66, 1017] 2 C2
14) [8, 14, 41] [1] 2 [8, 14, 41] 2 C2
15) [8, 18, 73] [1] 1 [8, 18, 73] 1 C1
16) [8, 26, 137] [1] 2 [8, 26, 137] 2 C2
17) [8, 22, 89] [1] 1 [8, 22, 89] 1 C1
18) [8, 30, 153] [1] 4 [8, 30, 153] 4 C2 x C2
19) [8, 38, 233] [1] 1 [8, 38, 233] 1 C1
20) [8, 10, 17] [1] 1 [8, 10, 17] 1 C1
21) [8, 34, 281] [1] 1 [8, 34, 281] 1 C1
22) [5, 66, 909] [1] 2 [5, 66, 909] 2 C2
23) [5, 21, 109] [1] 1 [5, 21, 109] 1 C1
24) [5, 41, 389] [1] 1 [5, 41, 389] 1 C1
25) [5, 17, 61] [1] 1 [5, 17, 61] 1 C1
26) [5, 34, 269] [1] 1 [5, 34, 269] 1 C1
27) [5, 13, 41] [1] 1 [5, 13, 41] 1 C1
28) [5, 26, 149] [1] 1 [5, 26, 149] 1 C1
29) [5, 11, 29] [1] 2 [5, 11, 29] 2 C2
30) [5, 33, 261] [1] 2 [5, 33, 261] 2 C2
31) [29, 26, 53] [1] 1 [29, 26, 53] 1 C1
32) [29, 7, 5] [1] 2 [29, 7, 5] 2 C2
33) [29, 21, 45] [1] 2 [29, 21, 45] 2 C2
34) [29, 9, 13] [1] 1 [29, 9, 13] 1 C1
35) [257, 23, 68] [1] 1 [257, 23, 68] 3 C3
36) [149, 13, 5] [1] 1 [149, 13, 5] 1 C1
37) [113, 33, 18] [1] 2 [113, 33, 18] 2 C2
38) [89, 11, 8] [1] 1 [89, 11, 8] 1 C1
39) [53, 13, 29] [1] 1 [53, 13, 29] 1 C1
40) [281, 17, 2] [1] 1 [281, 17, 2] 1 C1
41) [61, 9, 5] [1] 1 [61, 9, 5] 1 C1
42) [17, 5, 2] [1] 1 [17, 5, 2] 1 C1
43) [17, 15, 52] [2] 1 [17, 15, 52] 1 C1
44) [17, 47, 548] [1] 1 [17, 47, 548] 1 C1
45) [17, 15, 52] [1] 1 [17, 15, 52] 1 C1
46) [17, 46, 257] [1] 1 [17, 46, 257] 1 C1
47) [17, 25, 50] [1] 2 [17, 25, 50] 2 C2
48) [181, 41, 13] [1] 1 [181, 41, 13] 1 C1
49) [44, 14, 5] [1] 2 [44, 14, 5] 2 C2
50) [44, 8, 5] [1] 2 [44, 8, 5] 2 C2
51) [44, 42, 45] [1] 4 [44, 42, 45] 4 C2 x C2
52) [389, 37, 245] [1] 1 [389, 37, 245] 1 C1
53) [12, 50, 325] [1] 4 [12, 50, 325] 4 C2 x C2
54) [12, 10, 13] [1] 2 [12, 10, 13] 2 C2
55) [12, 26, 157] [1] 2 [12, 26, 157] 2 C2
56) [12, 8, 13] [1] 2 [12, 8, 13] 2 C2
57) [12, 26, 61] [1] 2 [12, 26, 61] 2 C2
58) [12, 14, 37] [1] 2 [12, 14, 37] 2 C2
59) [73, 9, 2] [1] 1 [73, 9, 2] 1 C1
60) [73, 47, 388] [1] 1 [73, 47, 388] 1 C1
61) [233, 19, 32] [1] 1 [233, 19, 32] 1 C1
62) [41, 11, 20] [1] 1 [41, 11, 20] 1 C1
63) [101, 33, 45] [1] 2 [101, 33, 45] 2 C2
64) [172, 34, 117] [1] 2 [172, 34, 117] 2 C2