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 364 Igusa CM invariants of non-normal (D4) fields: 36

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [344, 334, 26513] [1] 1 [344, 334, 26513] 182 C182
2) [629, 529, 13193] [1] 1 [629, 529, 13193] 364 C364
3) [236, 514, 19793] [1] 1 [236, 514, 19793] 182 C182
4) [205, 881, 189889] [1] 1 [205, 881, 189889] 364 C364
5) [13, 718, 112033] [1] 1 [13, 718, 112033] 182 C182
6) [76, 474, 36713] [1] 1 [76, 474, 36713] 182 C182
7) [76, 854, 179593] [1] 1 [76, 854, 179593] 182 C182
8) [29, 881, 192409] [1] 1 [29, 881, 192409] 182 C182
9) [24, 878, 188017] [1] 1 [24, 878, 188017] 182 C182
10) [781, 593, 72097] [1] 1 [781, 593, 72097] 182 C182
11) [40, 782, 139921] [1] 1 [40, 782, 139921] 364 C2 x C182
12) [1733, 157, 5729] [1] 1 [1733, 157, 5729] 182 C182
13) [37, 822, 159449] [1] 1 [37, 822, 159449] 182 C182
14) [949, 545, 72121] [1] 1 [949, 545, 72121] 364 C364
15) [293, 406, 22457] [1] 1 [293, 406, 22457] 182 C182
16) [61, 681, 106409] [1] 1 [61, 681, 106409] 182 C182
17) [17, 598, 76073] [1] 1 [17, 598, 76073] 182 C182
18) [17, 646, 71417] [1] 1 [17, 646, 71417] 182 C182
19) [997, 441, 6497] [1] 1 [997, 441, 6497] 182 C182
20) [573, 517, 3649] [1] 1 [573, 517, 3649] 182 C182
21) [181, 621, 68129] [1] 1 [181, 621, 68129] 182 C182
22) [1061, 481, 51209] [1] 1 [1061, 481, 51209] 182 C182
23) [1789, 129, 3713] [1] 1 [1789, 129, 3713] 182 C182
24) [1213, 377, 10969] [1] 1 [1213, 377, 10969] 182 C182
25) [613, 537, 16769] [1] 1 [613, 537, 16769] 182 C182
26) [12, 898, 197713] [1] 1 [12, 898, 197713] 182 C182
27) [21, 793, 154897] [1] 1 [21, 793, 154897] 182 C182
28) [85, 761, 135409] [1] 1 [85, 761, 135409] 364 C2 x C182
29) [85, 669, 98609] [1] 1 [85, 669, 98609] 364 C364
30) [365, 286, 14609] [1] 1 [365, 286, 14609] 364 C364
31) [101, 529, 51553] [1] 1 [101, 529, 51553] 182 C182
32) [101, 694, 94553] [1] 1 [101, 694, 94553] 182 C182
33) [172, 866, 181297] [1] 1 [172, 866, 181297] 182 C182
34) [265, 422, 6361] [1] 1 [265, 422, 6361] 364 C2 x C182
35) [69, 854, 177913] [1] 1 [69, 854, 177913] 182 C182
36) [488, 538, 13313] [1] 1 [488, 538, 13313] 364 C2 x C182