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 108 Igusa CM invariants of non-normal (D4) fields: 70

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [237, 97, 2293] [1] 1 [237, 97, 2293] 54 C54
2) [229, 97, 1837] [1] 1 [229, 97, 1837] 162 C3 x C54
3) [461, 281, 19625] [1] 1 [461, 281, 19625] 54 C54
4) [853, 85, 1593] [3] 1 [853, 85, 1593] 18 C18
5) [733, 141, 3321] [3] 2 [733, 141, 3321] 108 C6 x C18
6) [205, 109, 2509] [1] 1 [205, 109, 2509] 108 C108
7) [13, 1073, 114409] [1] 1 [13, 1073, 114409] 54 C54
8) [13, 477, 33401] [1] 1 [13, 477, 33401] 54 C54
9) [13, 350, 23137] [2] 1 [13, 350, 23137] 18 C18
10) [13, 165, 5633] [2, 2] 1 [13, 165, 5633] 18 C18
11) [8, 494, 53809] [1] 1 [8, 494, 53809] 54 C54
12) [8, 774, 141577] [1] 1 [8, 774, 141577] 54 C54
13) [8, 1050, 263457] [1] 2 [8, 1050, 263457] 108 C6 x C18
14) [8, 286, 20321] [1] 1 [8, 286, 20321] 54 C54
15) [8, 786, 104521] [1] 1 [8, 786, 104521] 54 C54
16) [8, 286, 19297] [1] 1 [8, 286, 19297] 54 C54
17) [8, 414, 34657] [1] 1 [8, 414, 34657] 54 C54
18) [8, 698, 71873] [1] 1 [8, 698, 71873] 54 C54
19) [8, 670, 73025] [1] 2 [8, 670, 73025] 108 C2 x C54
20) [8, 586, 82961] [1] 1 [8, 586, 82961] 54 C3 x C18
21) [8, 946, 223081] [1] 1 [8, 946, 223081] 54 C3 x C18
22) [8, 834, 98617] [1] 1 [8, 834, 98617] 54 C54
23) [5, 1569, 596529] [1] 2 [5, 1569, 596529] 108 C2 x C54
24) [5, 1129, 311249] [1] 1 [5, 1129, 311249] 54 C54
25) [5, 13, 41] [2, 38] 1 [5, 13, 41] 1 C1
26) [5, 1121, 295249] [1] 1 [5, 1121, 295249] 54 C54
27) [5, 374, 33689] [2, 2] 1 [5, 374, 33689] 18 C18
28) [5, 2334, 1240209] [1] 2 [5, 2334, 1240209] 108 C6 x C18
29) [5, 2529, 1342449] [1] 2 [5, 2529, 1342449] 108 C3 x C36
30) [5, 1229, 357449] [1] 1 [5, 1229, 357449] 54 C54
31) [5, 1006, 252689] [1] 1 [5, 1006, 252689] 54 C54
32) [5, 374, 31049] [2, 2] 1 [5, 374, 31049] 18 C18
33) [5, 2061, 968769] [1] 2 [5, 2061, 968769] 108 C3 x C36
34) [5, 2469, 1519929] [1] 2 [5, 2469, 1519929] 108 C2 x C54
35) [5, 1734, 648009] [1] 2 [5, 1734, 648009] 108 C2 x C54
36) [5, 1214, 322369] [1] 1 [5, 1214, 322369] 54 C54
37) [5, 861, 185329] [1] 1 [5, 861, 185329] 54 C54
38) [5, 901, 179489] [1] 1 [5, 901, 179489] 54 C3 x C18
39) [5, 1706, 675589] [1] 1 [5, 1706, 675589] 54 C54
40) [5, 1146, 272149] [1] 1 [5, 1146, 272149] 54 C54
41) [5, 2049, 925569] [1] 2 [5, 2049, 925569] 108 C3 x C36
42) [5, 326, 24569] [2, 2] 1 [5, 326, 24569] 18 C18
43) [5, 366, 32209] [2, 2] 1 [5, 366, 32209] 18 C18
44) [5, 2181, 1091889] [1] 2 [5, 2181, 1091889] 108 C108
45) [5, 1182, 342801] [1] 2 [5, 1182, 342801] 108 C2 x C54
46) [5, 1081, 252089] [1] 1 [5, 1081, 252089] 54 C54
47) [5, 886, 170329] [1] 1 [5, 886, 170329] 54 C3 x C18
48) [29, 278, 18857] [1] 1 [29, 278, 18857] 54 C54
49) [29, 125, 2681] [2, 2] 1 [29, 125, 2681] 18 C18
50) [29, 413, 41417] [1] 1 [29, 413, 41417] 54 C54
51) [24, 142, 4657] [1] 1 [24, 142, 4657] 54 C3 x C18
52) [40, 178, 7561] [1] 1 [40, 178, 7561] 108 C2 x C54
53) [509, 217, 1465] [1] 1 [509, 217, 1465] 54 C54
54) [53, 266, 15781] [1] 1 [53, 266, 15781] 54 C54
55) [33, 323, 14788] [1] 1 [33, 323, 14788] 54 C54
56) [61, 33, 257] [5] 1 [61, 33, 257] 9 C9
57) [17, 278, 5993] [2, 2] 1 [17, 278, 5993] 54 C54
58) [17, 278, 5993] [1] 1 [17, 278, 5993] 54 C54
59) [613, 181, 681] [1] 1 [613, 181, 681] 54 C54
60) [12, 710, 45337] [1] 1 [12, 710, 45337] 54 C54
61) [12, 398, 36529] [1] 1 [12, 398, 36529] 54 C54
62) [12, 890, 96457] [1] 1 [12, 890, 96457] 54 C54
63) [12, 818, 94273] [1] 1 [12, 818, 94273] 54 C3 x C18
64) [21, 121, 3529] [2, 2] 1 [21, 121, 3529] 18 C18
65) [21, 1310, 165601] [1] 1 [21, 1310, 165601] 54 C54
66) [85, 133, 2701] [1] 1 [85, 133, 2701] 108 C108
67) [41, 166, 985] [1] 1 [41, 166, 985] 54 C54
68) [41, 166, 985] [2, 2] 1 [41, 166, 985] 54 C54
69) [397, 301, 20169] [3] 1 [397, 301, 20169] 18 C18
70) [69, 278, 1657] [2, 2] 1 [69, 278, 1657] 18 C18