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 176 Igusa CM invariants of non-normal (D4) fields: 90

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [344, 444, 43780] [1] 2 [344, 444, 43780] 176 C2 x C2 x C44
2) [437, 345, 11293] [1] 1 [437, 345, 11293] 88 C88
3) [737, 255, 7228] [1] 1 [737, 255, 7228] 88 C2 x C44
4) [269, 369, 14605] [1] 1 [269, 369, 14605] 88 C2 x C44
5) [269, 753, 39465] [1] 2 [269, 753, 39465] 176 C2 x C88
6) [88, 100, 1708] [1] 1 [88, 100, 1708] 88 C2 x C44
7) [88, 442, 41713] [1] 1 [88, 442, 41713] 88 C2 x C44
8) [296, 492, 59332] [1] 1 [296, 492, 59332] 352 C2 x C4 x C44
9) [129, 382, 34417] [1] 1 [129, 382, 34417] 88 C88
10) [1033, 127, 1708] [1] 1 [1033, 127, 1708] 88 C2 x C44
11) [473, 327, 6748] [1] 1 [473, 327, 6748] 264 C2 x C132
12) [109, 686, 6033] [1] 1 [109, 686, 6033] 88 C88
13) [109, 373, 22765] [1] 1 [109, 373, 22765] 88 C2 x C44
14) [641, 287, 7612] [1] 1 [641, 287, 7612] 88 C2 x C44
15) [97, 571, 70816] [1] 1 [97, 571, 70816] 88 C88
16) [97, 287, 13584] [1] 1 [97, 287, 13584] 88 C88
17) [2381, 745, 4825] [1] 2 [2381, 745, 4825] 176 C2 x C88
18) [380, 456, 51604] [1] 2 [380, 456, 51604] 352 C2 x C4 x C44
19) [421, 433, 45925] [1] 1 [421, 433, 45925] 88 C88
20) [493, 961, 23697] [1] 1 [493, 961, 23697] 176 C176
21) [13, 529, 69229] [1] 1 [13, 529, 69229] 88 C88
22) [13, 565, 78373] [1] 1 [13, 565, 78373] 88 C88
23) [13, 1094, 282361] [1] 1 [13, 1094, 282361] 88 C88
24) [13, 469, 46537] [1] 1 [13, 469, 46537] 88 C88
25) [76, 304, 22420] [1] 2 [76, 304, 22420] 176 C2 x C2 x C44
26) [76, 322, 14977] [1] 1 [76, 322, 14977] 88 C2 x C44
27) [5, 1781, 775289] [1] 1 [5, 1781, 775289] 88 C88
28) [5, 1126, 281689] [1] 1 [5, 1126, 281689] 88 C88
29) [5, 1133, 309641] [1] 1 [5, 1133, 309641] 88 C88
30) [5, 1209, 312889] [1] 1 [5, 1209, 312889] 88 C88
31) [5, 1841, 846409] [1] 1 [5, 1841, 846409] 88 C88
32) [5, 897, 173401] [1] 1 [5, 897, 173401] 88 C88
33) [29, 445, 22529] [1] 1 [29, 445, 22529] 88 C88
34) [29, 429, 13465] [1] 1 [29, 429, 13465] 88 C88
35) [29, 1073, 65801] [1] 1 [29, 1073, 65801] 88 C88
36) [29, 462, 45937] [1] 1 [29, 462, 45937] 88 C88
37) [92, 474, 50281] [1] 1 [92, 474, 50281] 88 C2 x C44
38) [92, 446, 46417] [1] 1 [92, 446, 46417] 88 C2 x C44
39) [2117, 905, 115313] [1] 1 [2117, 905, 115313] 176 C176
40) [757, 1525, 526713] [1] 1 [757, 1525, 526713] 88 C88
41) [257, 407, 26956] [1] 1 [257, 407, 26956] 264 C2 x C132
42) [781, 957, 205337] [1] 1 [781, 957, 205337] 88 C88
43) [893, 1121, 99617] [1] 1 [893, 1121, 99617] 88 C2 x C44
44) [152, 444, 39556] [1] 2 [152, 444, 39556] 176 C2 x C2 x C44
45) [40, 466, 53929] [1] 1 [40, 466, 53929] 176 C2 x C2 x C44
46) [149, 561, 77749] [1] 1 [149, 561, 77749] 88 C2 x C44
47) [149, 318, 15745] [1] 1 [149, 318, 15745] 88 C2 x C44
48) [185, 471, 47644] [1] 1 [185, 471, 47644] 176 C4 x C44
49) [857, 207, 5356] [1] 1 [857, 207, 5356] 88 C2 x C44
50) [305, 471, 51724] [1] 1 [305, 471, 51724] 176 C4 x C44
51) [565, 345, 26225] [1] 1 [565, 345, 26225] 176 C176
52) [53, 168, 1756] [1] 1 [53, 168, 1756] 88 C88
53) [53, 790, 33913] [1] 1 [53, 790, 33913] 88 C88
54) [53, 414, 29281] [1] 1 [53, 414, 29281] 88 C2 x C44
55) [53, 689, 40121] [1] 1 [53, 689, 40121] 88 C88
56) [53, 222, 11473] [1] 1 [53, 222, 11473] 88 C2 x C44
57) [53, 777, 15769] [1] 1 [53, 777, 15769] 88 C88
58) [53, 621, 96397] [1] 1 [53, 621, 96397] 88 C2 x C44
59) [37, 1501, 524169] [1] 1 [37, 1501, 524169] 88 C88
60) [581, 333, 20605] [1] 1 [581, 333, 20605] 88 C2 x C44
61) [197, 369, 16261] [1] 1 [197, 369, 16261] 88 C2 x C44
62) [17, 359, 27592] [1] 1 [17, 359, 27592] 88 C88
63) [677, 269, 4381] [1] 1 [677, 269, 4381] 88 C88
64) [173, 71, 871] [1] 1 [173, 71, 871] 88 C2 x C44
65) [173, 429, 30397] [1] 1 [173, 429, 30397] 88 C88
66) [3373, 349, 9369] [1] 1 [3373, 349, 9369] 88 C88
67) [869, 201, 4669] [1] 1 [869, 201, 4669] 88 C2 x C44
68) [133, 361, 17917] [1] 1 [133, 361, 17917] 88 C2 x C44
69) [524, 368, 29140] [1] 2 [524, 368, 29140] 176 C2 x C2 x C44
70) [776, 242, 7657] [1] 1 [776, 242, 7657] 176 C4 x C44
71) [668, 296, 15892] [1] 2 [668, 296, 15892] 176 C4 x C44
72) [389, 341, 7189] [1] 1 [389, 341, 7189] 88 C2 x C44
73) [21, 577, 82597] [1] 1 [21, 577, 82597] 88 C88
74) [85, 265, 17365] [1] 1 [85, 265, 17365] 176 C4 x C44
75) [749, 261, 12349] [1] 1 [749, 261, 12349] 88 C2 x C44
76) [277, 717, 23193] [1] 1 [277, 717, 23193] 88 C88
77) [3221, 433, 39625] [1] 1 [3221, 433, 39625] 264 C264
78) [73, 391, 30172] [1] 1 [73, 391, 30172] 88 C2 x C44
79) [233, 507, 61408] [1] 1 [233, 507, 61408] 88 C2 x C44
80) [56, 602, 90097] [1] 1 [56, 602, 90097] 88 C2 x C44
81) [1889, 45, 34] [1] 1 [1889, 45, 34] 88 C88
82) [41, 643, 48740] [1] 1 [41, 643, 48740] 88 C88
83) [241, 955, 18276] [1] 1 [241, 955, 18276] 88 C88
84) [829, 1021, 6729] [1] 1 [829, 1021, 6729] 88 C88
85) [101, 1718, 712025] [1] 1 [101, 1718, 712025] 88 C88
86) [101, 1313, 396425] [1] 1 [101, 1313, 396425] 88 C88
87) [172, 286, 14257] [1] 1 [172, 286, 14257] 88 C88
88) [557, 309, 7021] [1] 1 [557, 309, 7021] 88 C2 x C44
89) [2341, 93, 1577] [1] 1 [2341, 93, 1577] 88 C88
90) [989, 153, 5605] [1] 1 [989, 153, 5605] 88 C2 x C44