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 416 Igusa CM invariants of non-normal (D4) fields: 48

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [661, 718, 118305] [1] 1 [661, 718, 118305] 208 C2 x C104
2) [157, 1045, 200433] [1] 1 [157, 1045, 200433] 208 C2 x C104
3) [3669, 209, 2665] [1] 1 [3669, 209, 2665] 208 C2 x C104
4) [301, 1677, 669897] [1] 1 [301, 1677, 669897] 208 C2 x C104
5) [449, 1118, 283745] [1] 1 [449, 1118, 283745] 208 C2 x C104
6) [473, 974, 116081] [1] 1 [473, 974, 116081] 624 C624
7) [213, 1005, 171513] [1] 1 [213, 1005, 171513] 208 C2 x C104
8) [3061, 493, 23265] [1] 1 [3061, 493, 23265] 208 C2 x C104
9) [205, 1126, 107049] [1] 1 [205, 1126, 107049] 416 C4 x C104
10) [1669, 1101, 209169] [1] 1 [1669, 1101, 209169] 208 C2 x C104
11) [2269, 853, 113265] [1] 1 [2269, 853, 113265] 208 C2 x C104
12) [309, 1749, 742425] [1] 1 [309, 1749, 742425] 208 C2 x C104
13) [309, 633, 66105] [1] 1 [309, 633, 66105] 208 C2 x C104
14) [1077, 1029, 5961] [1] 1 [1077, 1029, 5961] 208 C208
15) [421, 1357, 359217] [1] 1 [421, 1357, 359217] 208 C208
16) [821, 398, 26465] [1] 1 [821, 398, 26465] 208 C2 x C104
17) [13, 1630, 654033] [1] 1 [13, 1630, 654033] 208 C2 x C104
18) [8, 2026, 1026097] [1] 1 [8, 2026, 1026097] 208 C208
19) [8, 1802, 810833] [1] 1 [8, 1802, 810833] 208 C208
20) [5, 1973, 972401] [1] 1 [5, 1973, 972401] 208 C2 x C104
21) [5, 1633, 632641] [1] 1 [5, 1633, 632641] 208 C208
22) [29, 1601, 610169] [1] 1 [29, 1601, 610169] 208 C2 x C104
23) [93, 881, 188809] [1] 1 [93, 881, 188809] 208 C2 x C104
24) [757, 145, 3553] [1] 1 [757, 145, 3553] 208 C2 x C104
25) [3005, 505, 2905] [1] 1 [3005, 505, 2905] 416 C4 x C104
26) [3781, 157, 5217] [1] 1 [3781, 157, 5217] 208 C2 x C104
27) [2077, 1005, 247833] [1] 1 [2077, 1005, 247833] 208 C2 x C104
28) [1141, 1213, 216945] [1] 1 [1141, 1213, 216945] 208 C2 x C104
29) [149, 773, 59945] [1] 1 [149, 773, 59945] 208 C2 x C104
30) [53, 1049, 93721] [1] 1 [53, 1049, 93721] 208 C2 x C104
31) [1189, 121, 985] [1] 1 [1189, 121, 985] 416 C2 x C2 x C104
32) [1933, 997, 166833] [1] 1 [1933, 997, 166833] 208 C2 x C104
33) [37, 1414, 399801] [1] 1 [37, 1414, 399801] 208 C2 x C104
34) [37, 829, 149601] [1] 1 [37, 829, 149601] 208 C2 x C104
35) [37, 1441, 452289] [1] 1 [37, 1441, 452289] 208 C2 x C104
36) [1477, 141, 4601] [1] 1 [1477, 141, 4601] 208 C208
37) [61, 1173, 258201] [1] 1 [61, 1173, 258201] 208 C2 x C104
38) [61, 1229, 228145] [1] 1 [61, 1229, 228145] 208 C2 x C104
39) [373, 1861, 865737] [1] 1 [373, 1861, 865737] 208 C2 x C104
40) [2965, 565, 79065] [1] 1 [2965, 565, 79065] 416 C4 x C104
41) [997, 1465, 494433] [1] 1 [997, 1465, 494433] 208 C208
42) [869, 1249, 231625] [1] 1 [869, 1249, 231625] 208 C2 x C104
43) [1061, 1037, 13937] [1] 1 [1061, 1037, 13937] 208 C2 x C104
44) [12, 610, 92977] [1] 1 [12, 610, 92977] 208 C208
45) [21, 1997, 996577] [1] 1 [21, 1997, 996577] 208 C208
46) [397, 1429, 427041] [1] 1 [397, 1429, 427041] 208 C208
47) [1612, 1042, 110241] [1] 1 [1612, 1042, 110241] 416 C2 x C2 x C104
48) [553, 870, 109593] [1] 1 [553, 870, 109593] 208 C2 x C104