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 216 Igusa CM invariants of non-normal (D4) fields: 57

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 349, 23817] [1] 1 [157, 349, 23817] 108 C2 x C54
2) [301, 349, 28569] [1] 1 [301, 349, 28569] 108 C6 x C18
3) [629, 197, 9545] [1] 1 [629, 197, 9545] 216 C2 x C108
4) [349, 313, 20217] [1] 1 [349, 313, 20217] 108 C2 x C54
5) [461, 241, 5185] [1] 1 [461, 241, 5185] 108 C6 x C18
6) [461, 257, 10865] [1] 1 [461, 257, 10865] 108 C2 x C54
7) [797, 113, 2993] [1] 1 [797, 113, 2993] 108 C108
8) [13, 33, 113] [7, 63] 1 [13, 33, 113] 3 C3
9) [13, 942, 196673] [1] 1 [13, 942, 196673] 108 C6 x C18
10) [13, 2438, 810169] [1] 1 [13, 2438, 810169] 108 C108
11) [13, 918, 110009] [1] 1 [13, 918, 110009] 108 C108
12) [13, 382, 28993] [1] 1 [13, 382, 28993] 108 C108
13) [13, 406, 41001] [2, 2] 1 [13, 406, 41001] 36 C2 x C18
14) [13, 2222, 627793] [1] 1 [13, 2222, 627793] 108 C3 x C36
15) [8, 762, 143809] [1] 1 [8, 762, 143809] 108 C108
16) [8, 890, 175553] [1] 1 [8, 890, 175553] 108 C2 x C54
17) [8, 1146, 211201] [1] 1 [8, 1146, 211201] 108 C3 x C36
18) [8, 1002, 223153] [1] 1 [8, 1002, 223153] 108 C2 x C54
19) [8, 1434, 290977] [1] 1 [8, 1434, 290977] 108 C2 x C54
20) [5, 2521, 1494329] [1] 1 [5, 2521, 1494329] 108 C108
21) [5, 1077, 232201] [1] 1 [5, 1077, 232201] 108 C108
22) [5, 389, 37769] [7, 7] 1 [5, 389, 37769] 18 C18
23) [5, 2221, 1001009] [1] 1 [5, 2221, 1001009] 108 C108
24) [5, 1573, 612281] [1] 1 [5, 1573, 612281] 108 C3 x C36
25) [5, 1801, 789449] [1] 1 [5, 1801, 789449] 108 C108
26) [5, 2581, 1661609] [1] 1 [5, 2581, 1661609] 108 C108
27) [5, 2201, 1080689] [1] 1 [5, 2201, 1080689] 108 C108
28) [5, 1966, 873809] [1] 1 [5, 1966, 873809] 108 C108
29) [5, 1257, 333961] [1] 1 [5, 1257, 333961] 108 C108
30) [5, 150, 4905] [6, 6] 1 [5, 150, 4905] 12 C2 x C6
31) [5, 2326, 1183289] [1] 1 [5, 2326, 1183289] 108 C108
32) [5, 489, 59769] [3, 3] 1 [5, 489, 59769] 36 C2 x C18
33) [5, 2161, 962449] [1] 1 [5, 2161, 962449] 108 C108
34) [5, 1849, 849089] [1] 1 [5, 1849, 849089] 108 C108
35) [5, 1369, 456289] [1] 1 [5, 1369, 456289] 108 C2 x C54
36) [29, 446, 49265] [1] 1 [29, 446, 49265] 108 C2 x C54
37) [93, 405, 38193] [1] 1 [93, 405, 38193] 108 C2 x C54
38) [757, 133, 4233] [1] 1 [757, 133, 4233] 108 C2 x C54
39) [152, 338, 21113] [1] 1 [152, 338, 21113] 108 C108
40) [509, 381, 33109] [1] 1 [509, 381, 33109] 108 C108
41) [89, 262, 4345] [1] 1 [89, 262, 4345] 108 C2 x C54
42) [53, 485, 58793] [1] 1 [53, 485, 58793] 108 C2 x C54
43) [53, 461, 52481] [1] 1 [53, 461, 52481] 108 C2 x C54
44) [53, 425, 43553] [1] 1 [53, 425, 43553] 108 C108
45) [293, 281, 7361] [1] 1 [293, 281, 7361] 108 C108
46) [33, 374, 30217] [1] 1 [33, 374, 30217] 108 C2 x C54
47) [61, 33, 257] [15] 1 [61, 33, 257] 9 C9
48) [677, 169, 5617] [1] 1 [677, 169, 5617] 108 C108
49) [173, 477, 49573] [1] 1 [173, 477, 49573] 108 C108
50) [773, 125, 3713] [1] 1 [773, 125, 3713] 108 C108
51) [524, 218, 3497] [1] 1 [524, 218, 3497] 108 C108
52) [12, 1202, 343873] [1] 1 [12, 1202, 343873] 108 C2 x C54
53) [12, 550, 50233] [1] 1 [12, 550, 50233] 108 C2 x C54
54) [469, 253, 10257] [1] 1 [469, 253, 10257] 324 C6 x C54
55) [397, 289, 16017] [1] 1 [397, 289, 16017] 108 C2 x C54
56) [472, 274, 18297] [1] 1 [472, 274, 18297] 108 C108
57) [69, 197, 8305] [3, 3] 1 [69, 197, 8305] 36 C2 x C18