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 154 Igusa CM invariants of non-normal (D4) fields: 32

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [109, 521, 61729] [1] 1 [109, 521, 61729] 77 C77
2) [1669, 185, 4801] [1] 1 [1669, 185, 4801] 77 C77
3) [13, 645, 84737] [1] 1 [13, 645, 84737] 77 C77
4) [13, 678, 89753] [1] 1 [13, 678, 89753] 77 C77
5) [8, 1938, 582793] [1] 1 [8, 1938, 582793] 77 C77
6) [8, 830, 115777] [1] 1 [8, 830, 115777] 77 C77
7) [8, 2150, 598057] [1] 1 [8, 2150, 598057] 77 C77
8) [5, 817, 156521] [1] 1 [5, 817, 156521] 77 C77
9) [5, 637, 93241] [1] 1 [5, 637, 93241] 77 C77
10) [5, 2421, 1296949] [1] 1 [5, 2421, 1296949] 77 C77
11) [5, 889, 195049] [1] 1 [5, 889, 195049] 77 C77
12) [5, 817, 157841] [1] 1 [5, 817, 157841] 77 C77
13) [5, 1001, 250489] [1] 1 [5, 1001, 250489] 77 C77
14) [5, 797, 153841] [1] 1 [5, 797, 153841] 77 C77
15) [5, 737, 118681] [1] 1 [5, 737, 118681] 77 C77
16) [5, 737, 129841] [1] 1 [5, 737, 129841] 77 C77
17) [5, 1409, 479209] [1] 1 [5, 1409, 479209] 77 C77
18) [29, 745, 134921] [1] 1 [29, 745, 134921] 77 C77
19) [29, 1530, 579541] [1] 1 [29, 1530, 579541] 77 C77
20) [37, 393, 27281] [1] 1 [37, 393, 27281] 77 C77
21) [37, 277, 5113] [1] 1 [37, 277, 5113] 77 C77
22) [61, 614, 59113] [1] 1 [61, 614, 59113] 77 C77
23) [197, 502, 12569] [1] 1 [197, 502, 12569] 77 C77
24) [197, 901, 7477] [1] 1 [197, 901, 7477] 77 C77
25) [17, 307, 23524] [1] 1 [17, 307, 23524] 77 C77
26) [677, 505, 2657] [1] 1 [677, 505, 2657] 77 C77
27) [1213, 417, 43169] [1] 1 [1213, 417, 43169] 77 C77
28) [277, 741, 117257] [1] 1 [277, 741, 117257] 77 C77
29) [277, 521, 17377] [1] 1 [277, 521, 17377] 77 C77
30) [1193, 1063, 279808] [1] 1 [1193, 1063, 279808] 77 C77
31) [41, 2246, 670729] [1] 1 [41, 2246, 670729] 77 C77
32) [41, 354, 23293] [1] 1 [41, 354, 23293] 77 C77