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

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [1717, 165, 6377] [1] 1 [1717, 165, 6377] 420 C420
2) [157, 725, 114097] [1] 1 [157, 725, 114097] 210 C210
3) [237, 641, 71377] [1] 1 [237, 641, 71377] 210 C210
4) [301, 761, 127849] [1] 1 [301, 761, 127849] 210 C210
5) [629, 565, 34361] [1] 1 [629, 565, 34361] 420 C2 x C210
6) [88, 686, 89137] [1] 1 [88, 686, 89137] 210 C210
7) [205, 606, 88529] [1] 1 [205, 606, 88529] 420 C420
8) [253, 677, 86689] [1] 1 [253, 677, 86689] 210 C210
9) [253, 486, 42857] [1] 1 [253, 486, 42857] 210 C210
10) [844, 530, 39841] [1] 1 [844, 530, 39841] 210 C210
11) [1381, 329, 23953] [1] 1 [1381, 329, 23953] 210 C210
12) [1301, 349, 14513] [1] 1 [1301, 349, 14513] 210 C210
13) [93, 917, 207409] [1] 1 [93, 917, 207409] 210 C210
14) [1693, 177, 7409] [1] 1 [1693, 177, 7409] 210 C210
15) [757, 605, 76177] [1] 1 [757, 605, 76177] 210 C210
16) [24, 974, 237073] [1] 1 [24, 974, 237073] 210 C210
17) [24, 782, 143281] [1] 1 [24, 782, 143281] 210 C210
18) [40, 894, 195809] [1] 1 [40, 894, 195809] 420 C2 x C210
19) [973, 533, 68833] [1] 1 [973, 533, 68833] 210 C210
20) [113, 278, 17513] [1] 1 [113, 278, 17513] 210 C210
21) [565, 629, 67129] [1] 1 [565, 629, 67129] 420 C2 x C210
22) [533, 613, 55433] [1] 1 [533, 613, 55433] 420 C420
23) [341, 334, 22433] [1] 1 [341, 334, 22433] 210 C210
24) [37, 942, 221249] [1] 1 [37, 942, 221249] 210 C210
25) [321, 350, 10081] [1] 1 [321, 350, 10081] 630 C3 x C210
26) [949, 509, 45553] [1] 1 [949, 509, 45553] 420 C2 x C210
27) [293, 430, 41537] [1] 1 [293, 430, 41537] 210 C210
28) [197, 841, 168497] [1] 1 [197, 841, 168497] 210 C210
29) [173, 425, 45113] [1] 1 [173, 425, 45113] 210 C210
30) [573, 653, 82393] [1] 1 [573, 653, 82393] 210 C210
31) [133, 558, 24641] [1] 1 [133, 558, 24641] 210 C210
32) [1261, 389, 34993] [1] 1 [1261, 389, 34993] 420 C420
33) [77, 653, 98113] [1] 1 [77, 653, 98113] 210 C210
34) [77, 617, 74209] [1] 1 [77, 617, 74209] 210 C210
35) [653, 553, 29273] [1] 1 [653, 553, 29273] 210 C210
36) [44, 698, 96457] [1] 1 [44, 698, 96457] 210 C210
37) [44, 754, 127873] [1] 1 [44, 754, 127873] 210 C210
38) [1213, 413, 39913] [1] 1 [1213, 413, 39913] 210 C210
39) [389, 293, 16697] [1] 1 [389, 293, 16697] 210 C210
40) [12, 910, 205297] [1] 1 [12, 910, 205297] 210 C210
41) [12, 838, 171673] [1] 1 [12, 838, 171673] 210 C210
42) [21, 1009, 254473] [1] 1 [21, 1009, 254473] 210 C210
43) [85, 921, 209489] [1] 1 [85, 921, 209489] 420 C420
44) [85, 801, 152729] [1] 1 [85, 801, 152729] 420 C2 x C210
45) [277, 845, 172897] [1] 1 [277, 845, 172897] 210 C210
46) [73, 590, 44977] [1] 1 [73, 590, 44977] 210 C210
47) [469, 785, 153001] [1] 1 [469, 785, 153001] 630 C3 x C210
48) [469, 645, 70121] [1] 1 [469, 645, 70121] 630 C3 x C210
49) [101, 814, 164033] [1] 1 [101, 814, 164033] 210 C210
50) [69, 929, 213673] [1] 1 [69, 929, 213673] 210 C210