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 126 Igusa CM invariants of non-normal (D4) fields: 49

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [853, 485, 10825] [1] 2 [853, 485, 10825] 126 C126
2) [797, 65, 857] [1] 1 [797, 65, 857] 63 C63
3) [821, 613, 93737] [1] 1 [821, 613, 93737] 63 C63
4) [13, 977, 238369] [1] 1 [13, 977, 238369] 63 C63
5) [13, 878, 125329] [1] 1 [13, 878, 125329] 63 C63
6) [13, 385, 12457] [1] 1 [13, 385, 12457] 63 C63
7) [13, 941, 219937] [1] 1 [13, 941, 219937] 63 C63
8) [13, 486, 45737] [1] 1 [13, 486, 45737] 63 C63
9) [13, 1205, 292777] [1] 1 [13, 1205, 292777] 63 C63
10) [8, 1666, 459961] [1] 1 [8, 1666, 459961] 63 C63
11) [8, 378, 34369] [1] 1 [8, 378, 34369] 63 C63
12) [8, 2070, 546937] [1] 1 [8, 2070, 546937] 63 C63
13) [5, 769, 130729] [1] 1 [5, 769, 130729] 63 C63
14) [5, 862, 185441] [1] 1 [5, 862, 185441] 63 C63
15) [5, 806, 150889] [1] 1 [5, 806, 150889] 63 C63
16) [5, 821, 168409] [1] 1 [5, 821, 168409] 63 C3 x C21
17) [5, 821, 164449] [1] 1 [5, 821, 164449] 63 C3 x C21
18) [5, 757, 142601] [1] 1 [5, 757, 142601] 63 C63
19) [5, 2409, 1349289] [1] 2 [5, 2409, 1349289] 126 C126
20) [5, 926, 213649] [1] 1 [5, 926, 213649] 63 C63
21) [5, 1617, 534321] [1] 2 [5, 1617, 534321] 126 C126
22) [5, 941, 220009] [1] 1 [5, 941, 220009] 63 C63
23) [5, 961, 230729] [1] 1 [5, 961, 230729] 63 C63
24) [5, 493, 52561] [1] 1 [5, 493, 52561] 63 C63
25) [5, 1317, 424161] [1] 2 [5, 1317, 424161] 126 C126
26) [5, 997, 248441] [1] 1 [5, 997, 248441] 63 C63
27) [5, 2829, 1607409] [1] 2 [5, 2829, 1607409] 126 C126
28) [5, 1097, 296201] [1] 1 [5, 1097, 296201] 63 C63
29) [5, 697, 114041] [1] 1 [5, 697, 114041] 63 C63
30) [5, 901, 202889] [1] 1 [5, 901, 202889] 63 C3 x C21
31) [5, 1021, 260609] [1] 1 [5, 1021, 260609] 63 C63
32) [5, 2569, 1477889] [1] 2 [5, 2569, 1477889] 126 C126
33) [5, 2086, 989849] [1] 2 [5, 2086, 989849] 126 C126
34) [5, 1518, 530001] [1] 2 [5, 1518, 530001] 126 C126
35) [29, 553, 21577] [1] 1 [29, 553, 21577] 63 C63
36) [29, 894, 195633] [1] 2 [29, 894, 195633] 126 C126
37) [29, 661, 109049] [1] 1 [29, 661, 109049] 63 C63
38) [29, 313, 24137] [1] 1 [29, 313, 24137] 63 C63
39) [29, 581, 43609] [1] 1 [29, 581, 43609] 63 C63
40) [941, 57, 577] [1] 1 [941, 57, 577] 63 C63
41) [1901, 73, 857] [1] 1 [1901, 73, 857] 189 C3 x C63
42) [53, 278, 11689] [1] 1 [53, 278, 11689] 63 C63
43) [37, 190, 3697] [1] 1 [37, 190, 3697] 63 C63
44) [61, 381, 17609] [1] 1 [61, 381, 17609] 63 C63
45) [773, 525, 25425] [1] 4 [773, 525, 25425] 252 C2 x C126
46) [181, 453, 7817] [1] 1 [181, 453, 7817] 63 C63
47) [389, 769, 136073] [1] 1 [389, 769, 136073] 63 C63
48) [41, 430, 4241] [1] 1 [41, 430, 4241] 63 C63
49) [101, 214, 9833] [1] 1 [101, 214, 9833] 63 C63