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 196 Igusa CM invariants of non-normal (D4) fields: 74

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [236, 562, 2497] [1] 1 [236, 562, 2497] 98 C98
2) [88, 254, 15777] [1] 1 [88, 254, 15777] 98 C98
3) [104, 458, 6577] [1] 1 [104, 458, 6577] 196 C14 x C14
4) [205, 557, 40201] [1] 1 [205, 557, 40201] 196 C196
5) [685, 569, 42409] [1] 1 [685, 569, 42409] 196 C2 x C98
6) [517, 545, 17257] [1] 1 [517, 545, 17257] 98 C98
7) [13, 681, 108137] [1] 1 [13, 681, 108137] 98 C98
8) [13, 822, 158729] [1] 1 [13, 822, 158729] 98 C98
9) [13, 681, 86609] [1] 1 [13, 681, 86609] 98 C98
10) [8, 2182, 895369] [1] 1 [8, 2182, 895369] 98 C98
11) [8, 682, 114929] [1] 1 [8, 682, 114929] 98 C98
12) [8, 2566, 982537] [1] 1 [8, 2566, 982537] 98 C98
13) [5, 877, 187001] [1] 1 [5, 877, 187001] 98 C98
14) [5, 902, 200521] [1] 1 [5, 902, 200521] 98 C98
15) [5, 1273, 388021] [1] 1 [5, 1273, 388021] 98 C98
16) [5, 993, 243001] [1] 1 [5, 993, 243001] 98 C98
17) [5, 1753, 731701] [1] 1 [5, 1753, 731701] 98 C98
18) [5, 1806, 794929] [1] 1 [5, 1806, 794929] 98 C98
19) [29, 589, 80633] [1] 1 [29, 589, 80633] 98 C98
20) [29, 2170, 299221] [1] 1 [29, 2170, 299221] 98 C7 x C14
21) [29, 397, 30521] [1] 1 [29, 397, 30521] 98 C98
22) [24, 526, 47569] [1] 1 [24, 526, 47569] 98 C98
23) [24, 578, 47017] [1] 1 [24, 578, 47017] 98 C7 x C14
24) [24, 866, 182089] [1] 1 [24, 866, 182089] 98 C98
25) [24, 674, 87433] [1] 1 [24, 674, 87433] 98 C98
26) [1685, 177, 4041] [1] 2 [1685, 177, 4041] 392 C2 x C2 x C98
27) [1597, 221, 8617] [1] 1 [1597, 221, 8617] 98 C98
28) [781, 521, 23929] [1] 1 [781, 521, 23929] 98 C98
29) [40, 602, 47041] [1] 1 [40, 602, 47041] 196 C14 x C14
30) [40, 286, 7489] [1] 1 [40, 286, 7489] 196 C2 x C98
31) [40, 426, 33809] [1] 1 [40, 426, 33809] 196 C2 x C98
32) [149, 729, 116433] [1] 2 [149, 729, 116433] 196 C2 x C98
33) [113, 118, 1673] [1] 1 [113, 118, 1673] 98 C98
34) [89, 2310, 371401] [1] 1 [89, 2310, 371401] 98 C98
35) [53, 598, 88553] [1] 1 [53, 598, 88553] 98 C98
36) [53, 381, 14017] [1] 1 [53, 381, 14017] 98 C98
37) [37, 893, 197281] [1] 1 [37, 893, 197281] 98 C98
38) [33, 398, 20593] [1] 1 [33, 398, 20593] 98 C98
39) [17, 2678, 1166233] [1] 1 [17, 2678, 1166233] 98 C98
40) [17, 726, 109737] [1] 2 [17, 726, 109737] 196 C2 x C98
41) [17, 462, 43569] [1] 2 [17, 462, 43569] 196 C2 x C98
42) [373, 725, 110425] [1] 2 [373, 725, 110425] 196 C14 x C14
43) [173, 241, 11017] [1] 1 [173, 241, 11017] 98 C98
44) [173, 573, 50553] [1] 2 [173, 573, 50553] 196 C2 x C98
45) [181, 569, 47953] [1] 1 [181, 569, 47953] 98 C98
46) [133, 477, 24929] [1] 1 [133, 477, 24929] 98 C98
47) [1493, 265, 8225] [1] 2 [1493, 265, 8225] 196 C2 x C98
48) [44, 490, 48761] [1] 1 [44, 490, 48761] 98 C7 x C14
49) [44, 626, 58369] [1] 1 [44, 626, 58369] 98 C98
50) [44, 670, 111521] [1] 1 [44, 670, 111521] 98 C98
51) [44, 610, 84401] [1] 1 [44, 610, 84401] 98 C98
52) [389, 1457, 529837] [1] 1 [389, 1457, 529837] 98 C98
53) [389, 565, 28361] [1] 1 [389, 565, 28361] 98 C98
54) [12, 586, 42649] [1] 1 [12, 586, 42649] 98 C98
55) [12, 842, 172441] [1] 1 [12, 842, 172441] 98 C98
56) [12, 626, 95617] [1] 1 [12, 626, 95617] 98 C7 x C14
57) [12, 1846, 544729] [1] 1 [12, 1846, 544729] 98 C98
58) [12, 646, 69337] [1] 1 [12, 646, 69337] 98 C98
59) [12, 818, 166081] [1] 1 [12, 818, 166081] 98 C98
60) [12, 926, 214177] [1] 1 [12, 926, 214177] 98 C98
61) [12, 746, 119929] [1] 1 [12, 746, 119929] 98 C98
62) [21, 617, 65641] [1] 1 [21, 617, 65641] 98 C98
63) [21, 593, 83497] [1] 1 [21, 593, 83497] 98 C98
64) [21, 953, 226417] [1] 1 [21, 953, 226417] 98 C98
65) [21, 614, 82153] [1] 1 [21, 614, 82153] 98 C98
66) [21, 649, 75769] [1] 1 [21, 649, 75769] 98 C98
67) [21, 989, 244273] [1] 1 [21, 989, 244273] 98 C7 x C14
68) [85, 501, 42329] [1] 1 [85, 501, 42329] 196 C196
69) [85, 617, 79681] [1] 1 [85, 617, 79681] 196 C196
70) [277, 621, 59777] [1] 2 [277, 621, 59777] 196 C2 x C98
71) [485, 517, 2681] [1] 1 [485, 517, 2681] 196 C196
72) [41, 534, 18153] [1] 2 [41, 534, 18153] 196 C196
73) [69, 377, 14401] [1] 1 [69, 377, 14401] 98 C98
74) [69, 725, 122281] [1] 1 [69, 725, 122281] 98 C98