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 150 Igusa CM invariants of non-normal (D4) fields: 68

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 353, 31113] [1] 1 [157, 353, 31113] 75 C75
2) [157, 177, 7793] [1] 1 [157, 177, 7793] 75 C75
3) [449, 778, 135157] [1] 1 [449, 778, 135157] 75 C75
4) [137, 210, 10477] [1] 1 [137, 210, 10477] 75 C75
5) [137, 1455, 500452] [1] 1 [137, 1455, 500452] 75 C75
6) [97, 1087, 111844] [1] 1 [97, 1087, 111844] 75 C75
7) [13, 198, 8969] [2, 2] 1 [13, 198, 8969] 25 C25
8) [13, 222, 12113] [2, 2] 1 [13, 222, 12113] 25 C25
9) [13, 150, 5417] [2, 2] 1 [13, 150, 5417] 25 C25
10) [13, 244, 13012] [1] 2 [13, 244, 13012] 150 C150
11) [977, 963, 143668] [1] 1 [977, 963, 143668] 75 C75
12) [8, 1526, 540697] [1] 1 [8, 1526, 540697] 75 C75
13) [8, 462, 53233] [1] 1 [8, 462, 53233] 75 C75
14) [8, 1446, 460777] [1] 1 [8, 1446, 460777] 75 C75
15) [8, 1330, 421417] [1] 1 [8, 1330, 421417] 75 C5 x C15
16) [8, 1302, 386809] [1] 1 [8, 1302, 386809] 75 C75
17) [8, 1590, 626617] [1] 1 [8, 1590, 626617] 75 C75
18) [8, 1570, 604057] [1] 1 [8, 1570, 604057] 75 C75
19) [8, 1910, 911737] [1] 1 [8, 1910, 911737] 75 C75
20) [8, 1938, 938953] [1] 1 [8, 1938, 938953] 75 C75
21) [8, 1602, 617401] [1] 1 [8, 1602, 617401] 75 C75
22) [8, 1526, 574969] [1] 1 [8, 1526, 574969] 75 C75
23) [8, 1366, 465337] [1] 1 [8, 1366, 465337] 75 C75
24) [8, 1062, 205129] [1] 1 [8, 1062, 205129] 75 C75
25) [8, 1478, 538921] [1] 1 [8, 1478, 538921] 75 C75
26) [8, 398, 38449] [1] 1 [8, 398, 38449] 75 C75
27) [5, 1017, 236461] [1] 1 [5, 1017, 236461] 75 C75
28) [5, 468, 54676] [1] 2 [5, 468, 54676] 150 C150
29) [5, 1821, 825229] [1] 1 [5, 1821, 825229] 75 C5 x C15
30) [5, 1461, 507349] [1] 1 [5, 1461, 507349] 75 C75
31) [5, 1641, 651109] [1] 1 [5, 1641, 651109] 75 C75
32) [5, 1457, 486061] [1] 1 [5, 1457, 486061] 75 C75
33) [5, 1929, 930229] [1] 1 [5, 1929, 930229] 75 C75
34) [5, 1729, 744829] [1] 1 [5, 1729, 744829] 75 C75
35) [5, 1677, 685381] [1] 1 [5, 1677, 685381] 75 C75
36) [5, 1721, 739909] [1] 1 [5, 1721, 739909] 75 C75
37) [5, 1769, 775309] [1] 1 [5, 1769, 775309] 75 C75
38) [5, 193, 9281] [5, 5] 1 [5, 193, 9281] 15 C15
39) [5, 613, 84481] [1] 1 [5, 613, 84481] 75 C75
40) [5, 1921, 922549] [1] 1 [5, 1921, 922549] 75 C5 x C15
41) [5, 1197, 315421] [1] 1 [5, 1197, 315421] 75 C75
42) [29, 252, 15412] [1] 2 [29, 252, 15412] 150 C5 x C30
43) [149, 157, 4337] [1] 1 [149, 157, 4337] 75 C75
44) [113, 783, 90868] [1] 1 [113, 783, 90868] 75 C75
45) [1229, 965, 8821] [1] 1 [1229, 965, 8821] 225 C3 x C75
46) [89, 1399, 431428] [1] 1 [89, 1399, 431428] 75 C5 x C15
47) [89, 1070, 170881] [1] 1 [89, 1070, 170881] 75 C75
48) [53, 513, 28573] [1] 1 [53, 513, 28573] 75 C75
49) [281, 679, 114628] [1] 1 [281, 679, 114628] 75 C75
50) [281, 1119, 216868] [1] 1 [281, 1119, 216868] 75 C75
51) [61, 181, 8053] [1] 1 [61, 181, 8053] 75 C75
52) [197, 741, 28477] [1] 1 [197, 741, 28477] 75 C75
53) [3209, 335, 20836] [1] 1 [3209, 335, 20836] 75 C75
54) [17, 1710, 717697] [1] 1 [17, 1710, 717697] 75 C75
55) [17, 434, 46477] [1] 1 [17, 434, 46477] 75 C75
56) [17, 1391, 479092] [1] 1 [17, 1391, 479092] 75 C75
57) [17, 1630, 661777] [1] 1 [17, 1630, 661777] 75 C75
58) [17, 831, 163252] [1] 1 [17, 831, 163252] 75 C5 x C15
59) [1777, 491, 6516] [1] 1 [1777, 491, 6516] 75 C75
60) [181, 141, 2753] [1] 1 [181, 141, 2753] 75 C75
61) [44, 348, 25876] [1] 2 [44, 348, 25876] 150 C150
62) [44, 302, 19237] [1] 2 [44, 302, 19237] 150 C150
63) [44, 446, 49333] [1] 2 [44, 446, 49333] 150 C150
64) [73, 102, 1433] [2, 2] 1 [73, 102, 1433] 75 C75
65) [73, 102, 1433] [1] 1 [73, 102, 1433] 75 C75
66) [41, 1615, 625396] [1] 2 [41, 1615, 625396] 150 C150
67) [41, 1919, 920548] [1] 1 [41, 1919, 920548] 75 C75
68) [929, 999, 26308] [1] 1 [929, 999, 26308] 75 C5 x C15