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 352 Igusa CM invariants of non-normal (D4) fields: 94

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [2437, 745, 35793] [1] 1 [2437, 745, 35793] 176 C176
2) [317, 489, 59701] [1] 1 [317, 489, 59701] 176 C176
3) [157, 1969, 969201] [1] 1 [157, 1969, 969201] 176 C176
4) [157, 79, 1207] [1] 1 [157, 79, 1207] 176 C4 x C44
5) [3109, 493, 59985] [1] 1 [3109, 493, 59985] 176 C2 x C88
6) [1117, 1069, 50841] [1] 1 [1117, 1069, 50841] 176 C2 x C88
7) [229, 1302, 291897] [1] 1 [229, 1302, 291897] 528 C2 x C264
8) [301, 1717, 709857] [1] 1 [301, 1717, 709857] 176 C2 x C88
9) [269, 1913, 914825] [1] 1 [269, 1913, 914825] 176 C2 x C88
10) [269, 901, 66769] [1] 1 [269, 901, 66769] 176 C176
11) [236, 1574, 618425] [1] 1 [236, 1574, 618425] 176 C176
12) [349, 1861, 863649] [1] 1 [349, 1861, 863649] 176 C2 x C88
13) [120, 538, 69361] [1] 1 [120, 538, 69361] 352 C2 x C2 x C88
14) [461, 413, 41605] [1] 1 [461, 413, 41605] 176 C2 x C88
15) [213, 481, 51397] [1] 1 [213, 481, 51397] 176 C176
16) [161, 559, 39440] [1] 1 [161, 559, 39440] 176 C2 x C88
17) [109, 1126, 273369] [1] 1 [109, 1126, 273369] 176 C2 x C88
18) [109, 1438, 431505] [1] 1 [109, 1438, 431505] 176 C2 x C88
19) [813, 1461, 460257] [1] 1 [813, 1461, 460257] 176 C2 x C88
20) [797, 249, 15301] [1] 1 [797, 249, 15301] 176 C2 x C88
21) [97, 134, 2937] [1] 1 [97, 134, 2937] 176 C2 x C88
22) [733, 1137, 123633] [1] 1 [733, 1137, 123633] 528 C2 x C264
23) [205, 1041, 192969] [1] 1 [205, 1041, 192969] 352 C4 x C88
24) [1621, 133, 4017] [1] 1 [1621, 133, 4017] 176 C2 x C88
25) [2776, 642, 78057] [1] 1 [2776, 642, 78057] 176 C176
26) [209, 519, 64780] [1] 1 [209, 519, 64780] 176 C2 x C2 x C44
27) [13, 1585, 582033] [1] 1 [13, 1585, 582033] 176 C2 x C88
28) [13, 2017, 1016913] [1] 1 [13, 2017, 1016913] 176 C2 x C88
29) [8, 1102, 176593] [1] 1 [8, 1102, 176593] 176 C176
30) [5, 1558, 588841] [1] 1 [5, 1558, 588841] 176 C2 x C88
31) [5, 1438, 444961] [1] 1 [5, 1438, 444961] 176 C2 x C88
32) [29, 1661, 680849] [1] 1 [29, 1661, 680849] 176 C2 x C88
33) [941, 1033, 10585] [1] 1 [941, 1033, 10585] 176 C2 x C88
34) [2749, 649, 71625] [1] 1 [2749, 649, 71625] 176 C2 x C88
35) [440, 378, 24721] [1] 1 [440, 378, 24721] 352 C2 x C2 x C88
36) [93, 1617, 648441] [1] 1 [93, 1617, 648441] 176 C2 x C88
37) [93, 589, 86149] [1] 1 [93, 589, 86149] 176 C2 x C88
38) [93, 1214, 247921] [1] 1 [93, 1214, 247921] 176 C2 x C88
39) [93, 601, 90277] [1] 1 [93, 601, 90277] 176 C2 x C88
40) [24, 1586, 580249] [1] 1 [24, 1586, 580249] 176 C176
41) [24, 1586, 623449] [1] 1 [24, 1586, 623449] 176 C176
42) [221, 1574, 605225] [1] 1 [221, 1574, 605225] 352 C4 x C88
43) [877, 205, 8533] [1] 1 [877, 205, 8533] 176 C2 x C88
44) [285, 481, 54349] [1] 1 [285, 481, 54349] 352 C4 x C88
45) [105, 583, 84316] [1] 1 [105, 583, 84316] 352 C4 x C88
46) [1333, 1069, 77409] [1] 1 [1333, 1069, 77409] 176 C2 x C88
47) [152, 570, 81073] [1] 1 [152, 570, 81073] 176 C4 x C44
48) [149, 961, 155449] [1] 1 [149, 961, 155449] 176 C2 x C88
49) [1541, 1165, 252625] [1] 1 [1541, 1165, 252625] 176 C2 x C88
50) [53, 1541, 580937] [1] 1 [53, 1541, 580937] 176 C2 x C88
51) [53, 721, 95497] [1] 1 [53, 721, 95497] 176 C2 x C88
52) [957, 169, 6901] [1] 1 [957, 169, 6901] 352 C2 x C2 x C88
53) [1909, 117, 2945] [1] 1 [1909, 117, 2945] 176 C2 x C88
54) [2236, 898, 165825] [1] 1 [2236, 898, 165825] 352 C2 x C176
55) [37, 2005, 1004553] [1] 1 [37, 2005, 1004553] 176 C2 x C88
56) [37, 409, 37741] [1] 1 [37, 409, 37741] 176 C2 x C88
57) [364, 394, 25705] [1] 1 [364, 394, 25705] 352 C4 x C88
58) [293, 489, 57949] [1] 1 [293, 489, 57949] 176 C176
59) [465, 391, 32524] [1] 1 [465, 391, 32524] 352 C4 x C88
60) [537, 966, 224697] [1] 1 [537, 966, 224697] 176 C176
61) [501, 373, 28645] [1] 1 [501, 373, 28645] 176 C2 x C88
62) [33, 803, 121924] [1] 1 [33, 803, 121924] 176 C2 x C88
63) [61, 1201, 296169] [1] 1 [61, 1201, 296169] 176 C2 x C88
64) [61, 1409, 396265] [1] 1 [61, 1409, 396265] 176 C2 x C88
65) [61, 1661, 658849] [1] 1 [61, 1661, 658849] 176 C176
66) [61, 1257, 371817] [1] 1 [61, 1257, 371817] 176 C2 x C88
67) [1101, 1385, 417625] [1] 1 [1101, 1385, 417625] 528 C2 x C264
68) [677, 297, 17821] [1] 1 [677, 297, 17821] 176 C176
69) [173, 294, 18841] [1] 1 [173, 294, 18841] 176 C176
70) [2069, 1009, 249865] [1] 1 [2069, 1009, 249865] 176 C2 x C88
71) [232, 370, 15433] [1] 1 [232, 370, 15433] 352 C4 x C88
72) [133, 1437, 480033] [1] 1 [133, 1437, 480033] 176 C2 x C88
73) [77, 1094, 91001] [1] 1 [77, 1094, 91001] 176 C2 x C88
74) [77, 709, 75601] [1] 1 [77, 709, 75601] 176 C2 x C88
75) [1213, 1429, 502929] [1] 1 [1213, 1429, 502929] 176 C176
76) [21, 1382, 368617] [1] 1 [21, 1382, 368617] 176 C176
77) [21, 1277, 399697] [1] 1 [21, 1277, 399697] 176 C176
78) [21, 1534, 103105] [1] 1 [21, 1534, 103105] 176 C2 x C88
79) [21, 1718, 710665] [1] 1 [21, 1718, 710665] 176 C2 x C88
80) [85, 2005, 1004985] [1] 1 [85, 2005, 1004985] 352 C4 x C88
81) [277, 1689, 682641] [1] 1 [277, 1689, 682641] 176 C2 x C88
82) [1181, 1093, 83425] [1] 1 [1181, 1093, 83425] 176 C176
83) [485, 381, 30349] [1] 1 [485, 381, 30349] 352 C2 x C2 x C2 x C44
84) [1349, 1153, 183625] [1] 1 [1349, 1153, 183625] 176 C2 x C88
85) [829, 382, 23217] [1] 1 [829, 382, 23217] 176 C2 x C88
86) [2101, 997, 247977] [1] 1 [2101, 997, 247977] 528 C528
87) [397, 201, 10001] [1] 1 [397, 201, 10001] 176 C176
88) [397, 337, 6061] [1] 1 [397, 337, 6061] 176 C2 x C88
89) [365, 425, 37765] [1] 1 [365, 425, 37765] 352 C2 x C4 x C44
90) [472, 1474, 463401] [1] 1 [472, 1474, 463401] 176 C176
91) [101, 797, 98177] [1] 1 [101, 797, 98177] 176 C176
92) [557, 806, 19817] [1] 1 [557, 806, 19817] 176 C2 x C88
93) [2589, 749, 134425] [1] 1 [2589, 749, 134425] 528 C528
94) [717, 1005, 7113] [1] 1 [717, 1005, 7113] 176 C176