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 392 Igusa CM invariants of non-normal (D4) fields: 79

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [165, 677, 92761] [1] 1 [165, 677, 92761] 392 C2 x C196
2) [165, 686, 115009] [1] 1 [165, 686, 115009] 392 C2 x C196
3) [237, 725, 110017] [1] 1 [237, 725, 110017] 196 C196
4) [237, 541, 29977] [1] 1 [237, 541, 29977] 196 C196
5) [60, 526, 60529] [1] 1 [60, 526, 60529] 392 C2 x C196
6) [229, 905, 204241] [1] 1 [229, 905, 204241] 588 C588
7) [376, 270, 16721] [1] 1 [376, 270, 16721] 196 C2 x C98
8) [88, 830, 169057] [1] 1 [88, 830, 169057] 196 C2 x C98
9) [988, 458, 16873] [1] 1 [988, 458, 16873] 392 C2 x C196
10) [296, 382, 6881] [1] 1 [296, 382, 6881] 392 C2 x C2 x C98
11) [296, 430, 45041] [1] 1 [296, 430, 45041] 392 C2 x C2 x C98
12) [129, 566, 28489] [1] 1 [129, 566, 28489] 196 C196
13) [213, 566, 66457] [1] 1 [213, 566, 66457] 196 C196
14) [109, 734, 118993] [1] 1 [109, 734, 118993] 196 C2 x C98
15) [109, 489, 33593] [1] 1 [109, 489, 33593] 196 C196
16) [733, 513, 12833] [1] 1 [733, 513, 12833] 588 C588
17) [205, 609, 60689] [1] 1 [205, 609, 60689] 392 C2 x C196
18) [309, 725, 109081] [1] 1 [309, 725, 109081] 196 C196
19) [309, 785, 141001] [1] 1 [309, 785, 141001] 196 C196
20) [309, 557, 29281] [1] 1 [309, 557, 29281] 196 C14 x C14
21) [1077, 425, 12577] [1] 1 [1077, 425, 12577] 196 C7 x C28
22) [1336, 338, 16537] [1] 1 [1336, 338, 16537] 196 C2 x C98
23) [13, 745, 125857] [1] 1 [13, 745, 125857] 196 C196
24) [76, 914, 206113] [1] 1 [76, 914, 206113] 196 C2 x C98
25) [76, 630, 62441] [1] 1 [76, 630, 62441] 196 C2 x C98
26) [8, 986, 242977] [1] 1 [8, 986, 242977] 196 C2 x C98
27) [93, 613, 76993] [1] 1 [93, 613, 76993] 196 C2 x C98
28) [93, 977, 238609] [1] 1 [93, 977, 238609] 196 C2 x C98
29) [93, 953, 225913] [1] 1 [93, 953, 225913] 196 C2 x C98
30) [93, 830, 170737] [1] 1 [93, 830, 170737] 196 C196
31) [93, 433, 21553] [1] 1 [93, 433, 21553] 196 C196
32) [1357, 341, 26017] [1] 1 [1357, 341, 26017] 196 C196
33) [24, 562, 30361] [1] 1 [24, 562, 30361] 196 C2 x C98
34) [24, 574, 74593] [1] 1 [24, 574, 74593] 196 C2 x C98
35) [285, 701, 97129] [1] 1 [285, 701, 97129] 392 C2 x C196
36) [105, 526, 8689] [1] 1 [105, 526, 8689] 392 C2 x C2 x C98
37) [105, 182, 6601] [1] 1 [105, 182, 6601] 392 C2 x C196
38) [141, 377, 27601] [1] 1 [141, 377, 27601] 196 C196
39) [141, 893, 195097] [1] 1 [141, 893, 195097] 196 C2 x C98
40) [40, 666, 104129] [1] 1 [40, 666, 104129] 392 C2 x C2 x C98
41) [140, 362, 12601] [1] 1 [140, 362, 12601] 392 C2 x C2 x C98
42) [168, 526, 14737] [1] 1 [168, 526, 14737] 392 C2 x C2 x C98
43) [156, 314, 19033] [1] 1 [156, 314, 19033] 392 C2 x C196
44) [156, 554, 46153] [1] 1 [156, 554, 46153] 392 C2 x C2 x C98
45) [53, 937, 217889] [1] 1 [53, 937, 217889] 196 C2 x C98
46) [1189, 425, 42481] [1] 1 [1189, 425, 42481] 392 C2 x C2 x C98
47) [341, 589, 41633] [1] 1 [341, 589, 41633] 196 C2 x C98
48) [184, 638, 95137] [1] 1 [184, 638, 95137] 196 C2 x C98
49) [184, 770, 133321] [1] 1 [184, 770, 133321] 196 C196
50) [184, 482, 16681] [1] 1 [184, 482, 16681] 196 C14 x C14
51) [37, 678, 100121] [1] 1 [37, 678, 100121] 196 C196
52) [28, 798, 158753] [1] 1 [28, 798, 158753] 196 C2 x C98
53) [28, 642, 91841] [1] 1 [28, 642, 91841] 196 C196
54) [28, 666, 108089] [1] 1 [28, 666, 108089] 196 C196
55) [316, 578, 38017] [1] 1 [316, 578, 38017] 588 C14 x C42
56) [501, 761, 141649] [1] 1 [501, 761, 141649] 196 C7 x C28
57) [204, 566, 59689] [1] 1 [204, 566, 59689] 392 C2 x C196
58) [33, 422, 39769] [1] 1 [33, 422, 39769] 196 C196
59) [1757, 145, 4817] [1] 1 [1757, 145, 4817] 196 C196
60) [677, 541, 24257] [1] 1 [677, 541, 24257] 196 C196
61) [173, 670, 109457] [1] 1 [173, 670, 109457] 196 C196
62) [77, 565, 63617] [1] 1 [77, 565, 63617] 196 C196
63) [77, 742, 117929] [1] 1 [77, 742, 117929] 196 C2 x C98
64) [389, 517, 6041] [1] 1 [389, 517, 6041] 196 C196
65) [613, 301, 10237] [1] 1 [613, 301, 10237] 196 C196
66) [12, 682, 100729] [1] 1 [12, 682, 100729] 196 C2 x C98
67) [1293, 353, 15313] [1] 1 [1293, 353, 15313] 196 C196
68) [85, 977, 238441] [1] 1 [85, 977, 238441] 392 C2 x C196
69) [616, 554, 26833] [1] 1 [616, 554, 26833] 392 C2 x C196
70) [73, 422, 34009] [1] 1 [73, 422, 34009] 196 C196
71) [1517, 253, 6521] [1] 1 [1517, 253, 6521] 392 C14 x C28
72) [1580, 226, 6449] [1] 1 [1580, 226, 6449] 392 C2 x C2 x C98
73) [469, 569, 29233] [1] 1 [469, 569, 29233] 588 C2 x C294
74) [424, 174, 5873] [1] 1 [424, 174, 5873] 392 C2 x C2 x C98
75) [101, 961, 230249] [1] 1 [101, 961, 230249] 196 C196
76) [1324, 330, 6041] [1] 1 [1324, 330, 6041] 196 C2 x C98
77) [69, 598, 49657] [1] 1 [69, 598, 49657] 196 C2 x C98
78) [69, 758, 125977] [1] 1 [69, 758, 125977] 196 C2 x C98
79) [69, 454, 41593] [1] 1 [69, 454, 41593] 196 C196