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 50 Igusa CM invariants of non-normal (D4) fields: 76

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [229, 117, 617] [1] 1 [229, 117, 617] 75 C75
2) [409, 103, 1732] [1] 1 [409, 103, 1732] 25 C25
3) [269, 109, 1289] [1] 1 [269, 109, 1289] 25 C25
4) [137, 607, 22756] [1] 1 [137, 607, 22756] 25 C25
5) [1964, 726, 82669] [1] 2 [1964, 726, 82669] 50 C50
6) [109, 161, 4273] [1] 1 [109, 161, 4273] 25 C25
7) [97, 223, 10468] [1] 1 [97, 223, 10468] 25 C25
8) [1709, 753, 18277] [1] 1 [1709, 753, 18277] 25 C25
9) [13, 198, 8969] [1] 1 [13, 198, 8969] 25 C25
10) [13, 189, 8537] [1] 1 [13, 189, 8537] 25 C25
11) [13, 150, 5417] [1] 1 [13, 150, 5417] 25 C25
12) [13, 222, 12113] [1] 1 [13, 222, 12113] 25 C25
13) [8, 282, 19081] [1] 2 [8, 282, 19081] 50 C50
14) [8, 1078, 151129] [1] 2 [8, 1078, 151129] 50 C50
15) [8, 1298, 342793] [1] 2 [8, 1298, 342793] 50 C50
16) [8, 1110, 268825] [1] 2 [8, 1110, 268825] 50 C5 x C10
17) [8, 482, 52249] [1] 1 [8, 482, 52249] 25 C25
18) [8, 498, 59113] [1] 1 [8, 498, 59113] 25 C5 x C5
19) [8, 594, 70537] [1] 1 [8, 594, 70537] 25 C25
20) [8, 518, 48649] [1] 1 [8, 518, 48649] 25 C5 x C5
21) [8, 410, 41737] [1] 2 [8, 410, 41737] 50 C50
22) [8, 618, 70393] [1] 2 [8, 618, 70393] 50 C50
23) [8, 658, 63241] [1] 1 [8, 658, 63241] 25 C5 x C5
24) [8, 314, 17449] [1] 2 [8, 314, 17449] 50 C50
25) [8, 222, 10273] [1] 1 [8, 222, 10273] 25 C25
26) [8, 978, 121993] [1] 1 [8, 978, 121993] 25 C25
27) [8, 154, 5281] [1] 1 [8, 154, 5281] 25 C25
28) [5, 417, 37861] [1] 1 [5, 417, 37861] 25 C5 x C5
29) [5, 481, 56929] [1] 1 [5, 481, 56929] 25 C25
30) [5, 191, 9109] [1] 2 [5, 191, 9109] 50 C50
31) [5, 453, 50101] [1] 1 [5, 453, 50101] 25 C25
32) [5, 53, 641] [5, 5] 1 [5, 53, 641] 5 C5
33) [5, 276, 17044] [1] 2 [5, 276, 17044] 50 C50
34) [5, 333, 22441] [1] 1 [5, 333, 22441] 25 C25
35) [5, 641, 99469] [1] 1 [5, 641, 99469] 25 C5 x C5
36) [5, 741, 125509] [1] 1 [5, 741, 125509] 25 C25
37) [5, 13, 41] [15, 15] 2 [5, 13, 41] 1 C1
38) [5, 1309, 414589] [1] 2 [5, 1309, 414589] 50 C50
39) [5, 374, 32089] [1] 1 [5, 374, 32089] 25 C25
40) [5, 183, 8221] [1] 2 [5, 183, 8221] 50 C50
41) [5, 206, 10429] [1] 2 [5, 206, 10429] 50 C50
42) [5, 253, 16001] [1] 1 [5, 253, 16001] 25 C25
43) [5, 317, 20161] [1] 1 [5, 317, 20161] 25 C25
44) [5, 741, 134269] [1] 1 [5, 741, 134269] 25 C25
45) [5, 378, 35221] [1] 1 [5, 378, 35221] 25 C25
46) [29, 266, 8293] [1] 1 [29, 266, 8293] 25 C25
47) [29, 629, 80053] [1] 2 [29, 629, 80053] 50 C50
48) [29, 273, 2617] [1] 1 [29, 273, 2617] 25 C25
49) [29, 189, 8053] [1] 1 [29, 189, 8053] 25 C25
50) [29, 237, 13977] [1] 2 [29, 237, 13977] 50 C50
51) [257, 91, 1492] [1] 1 [257, 91, 1492] 75 C75
52) [2281, 223, 7300] [1] 1 [2281, 223, 7300] 25 C25
53) [2953, 463, 46948] [1] 1 [2953, 463, 46948] 25 C25
54) [89, 334, 15073] [1] 1 [89, 334, 15073] 25 C25
55) [53, 205, 9857] [1] 1 [53, 205, 9857] 25 C5 x C5
56) [37, 250, 3637] [1] 1 [37, 250, 3637] 25 C25
57) [293, 105, 2097] [1] 2 [293, 105, 2097] 50 C50
58) [293, 97, 521] [1] 1 [293, 97, 521] 25 C25
59) [61, 221, 12073] [1] 1 [61, 221, 12073] 25 C25
60) [197, 90, 1237] [1] 1 [197, 90, 1237] 25 C25
61) [3413, 237, 13189] [1] 1 [3413, 237, 13189] 25 C25
62) [17, 150, 3177] [2, 2] 2 [17, 150, 3177] 50 C50
63) [17, 710, 37897] [1] 1 [17, 710, 37897] 25 C25
64) [17, 1095, 297508] [1] 1 [17, 1095, 297508] 25 C25
65) [17, 150, 3177] [1] 2 [17, 150, 3177] 50 C50
66) [17, 483, 56788] [1] 1 [17, 483, 56788] 25 C25
67) [677, 135, 325] [1] 4 [677, 135, 325] 100 C2 x C50
68) [2909, 465, 18421] [1] 1 [2909, 465, 18421] 25 C25
69) [1481, 151, 2368] [1] 1 [1481, 151, 2368] 25 C25
70) [44, 464, 21748] [1] 2 [44, 464, 21748] 50 C50
71) [44, 222, 6997] [1] 2 [44, 222, 6997] 50 C50
72) [41, 911, 186724] [1] 1 [41, 911, 186724] 25 C25
73) [2213, 825, 156325] [1] 2 [2213, 825, 156325] 150 C5 x C30
74) [353, 319, 5584] [1] 1 [353, 319, 5584] 25 C25
75) [101, 369, 3109] [1] 1 [101, 369, 3109] 25 C5 x C5
76) [172, 224, 8244] [1] 2 [172, 224, 8244] 50 C50