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 30 Igusa CM invariants of non-normal (D4) fields: 95

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [3761, 63, 52] [1] 1 [3761, 63, 52] 15 C15
2) [157, 154, 277] [1] 1 [157, 154, 277] 15 C15
3) [137, 231, 12484] [1] 1 [137, 231, 12484] 15 C15
4) [137, 519, 20452] [1] 1 [137, 519, 20452] 15 C15
5) [109, 37, 97] [1] 1 [109, 37, 97] 15 C15
6) [1621, 121, 13] [1] 1 [1621, 121, 13] 15 C15
7) [421, 45, 401] [1] 1 [421, 45, 401] 15 C15
8) [1409, 527, 40900] [1] 1 [1409, 527, 40900] 15 C15
9) [13, 93, 2081] [1] 1 [13, 93, 2081] 15 C15
10) [13, 97, 1621] [1] 1 [13, 97, 1621] 15 C15
11) [13, 165, 6257] [1] 1 [13, 165, 6257] 15 C15
12) [13, 209, 10657] [1] 1 [13, 209, 10657] 15 C15
13) [13, 134, 2617] [2, 2] 1 [13, 134, 2617] 5 C5
14) [8, 282, 18313] [1] 2 [8, 282, 18313] 30 C30
15) [8, 390, 35977] [1] 1 [8, 390, 35977] 15 C15
16) [8, 950, 121657] [1] 2 [8, 950, 121657] 30 C30
17) [8, 310, 19417] [1] 1 [8, 310, 19417] 15 C15
18) [8, 294, 13417] [1] 1 [8, 294, 13417] 15 C15
19) [8, 570, 80425] [1] 4 [8, 570, 80425] 60 C2 x C30
20) [8, 342, 26041] [1] 1 [8, 342, 26041] 15 C15
21) [8, 226, 12697] [1] 1 [8, 226, 12697] 15 C15
22) [8, 198, 9769] [1] 1 [8, 198, 9769] 15 C15
23) [8, 482, 32089] [1] 1 [8, 482, 32089] 15 C15
24) [8, 222, 11353] [1] 2 [8, 222, 11353] 30 C30
25) [5, 57, 661] [5, 5] 1 [5, 57, 661] 3 C3
26) [5, 193, 9161] [1] 1 [5, 193, 9161] 15 C15
27) [5, 173, 6121] [1] 1 [5, 173, 6121] 15 C15
28) [5, 42, 421] [2, 2, 4] 2 [5, 42, 421] 3 C3
29) [5, 169, 7129] [1] 1 [5, 169, 7129] 15 C15
30) [5, 174, 6849] [2, 2] 2 [5, 174, 6849] 10 C10
31) [5, 94, 1889] [2, 2] 1 [5, 94, 1889] 5 C5
32) [5, 386, 32749] [1] 1 [5, 386, 32749] 15 C15
33) [5, 81, 1609] [2, 2] 1 [5, 81, 1609] 5 C5
34) [5, 202, 8581] [1] 1 [5, 202, 8581] 15 C15
35) [5, 149, 4889] [2, 2] 1 [5, 149, 4889] 5 C5
36) [5, 237, 13381] [1] 1 [5, 237, 13381] 15 C15
37) [5, 193, 9281] [1] 1 [5, 193, 9281] 15 C15
38) [5, 314, 23029] [1] 1 [5, 314, 23029] 15 C15
39) [5, 209, 10369] [1] 1 [5, 209, 10369] 15 C15
40) [5, 214, 11369] [1] 1 [5, 214, 11369] 15 C15
41) [5, 229, 13049] [1] 1 [5, 229, 13049] 15 C15
42) [5, 229, 13009] [1] 1 [5, 229, 13009] 15 C15
43) [5, 474, 56149] [1] 1 [5, 474, 56149] 15 C15
44) [5, 153, 5641] [1] 1 [5, 153, 5641] 15 C15
45) [5, 609, 91189] [1] 2 [5, 609, 91189] 30 C30
46) [5, 317, 21061] [1] 1 [5, 317, 21061] 15 C15
47) [5, 381, 35509] [1] 1 [5, 381, 35509] 15 C15
48) [5, 241, 14489] [1] 1 [5, 241, 14489] 15 C15
49) [5, 238, 14081] [1] 1 [5, 238, 14081] 15 C15
50) [5, 394, 38629] [1] 1 [5, 394, 38629] 15 C15
51) [5, 42, 421] [2, 2] 1 [5, 42, 421] 3 C3
52) [5, 354, 30829] [1] 1 [5, 354, 30829] 15 C15
53) [5, 158, 5521] [1] 1 [5, 158, 5521] 15 C15
54) [5, 42, 421] [2, 2, 2] 2 [5, 42, 421] 3 C3
55) [5, 621, 95749] [1] 2 [5, 621, 95749] 30 C30
56) [29, 93, 937] [1] 1 [29, 93, 937] 15 C15
57) [29, 685, 18061] [1] 1 [29, 685, 18061] 15 C15
58) [29, 157, 4937] [1] 1 [29, 157, 4937] 15 C15
59) [29, 177, 7477] [1] 1 [29, 177, 7477] 15 C15
60) [29, 159, 1789] [1] 2 [29, 159, 1789] 30 C30
61) [29, 39, 373] [1] 2 [29, 39, 373] 30 C30
62) [29, 141, 4093] [1] 1 [29, 141, 4093] 15 C15
63) [1613, 645, 93925] [1] 2 [1613, 645, 93925] 30 C30
64) [953, 243, 3088] [1] 1 [953, 243, 3088] 15 C15
65) [149, 81, 709] [1] 1 [149, 81, 709] 15 C15
66) [149, 170, 1861] [1] 1 [149, 170, 1861] 15 C15
67) [509, 91, 925] [1] 2 [509, 91, 925] 30 C30
68) [89, 130, 1021] [1] 1 [89, 130, 1021] 15 C15
69) [53, 585, 6997] [1] 1 [53, 585, 6997] 15 C15
70) [53, 41, 89] [2, 2] 1 [53, 41, 89] 5 C5
71) [281, 71, 628] [1] 1 [281, 71, 628] 15 C15
72) [281, 71, 628] [2] 1 [281, 71, 628] 15 C15
73) [37, 150, 3257] [1] 1 [37, 150, 3257] 15 C15
74) [293, 65, 397] [1] 1 [293, 65, 397] 15 C15
75) [61, 185, 7321] [1] 1 [61, 185, 7321] 15 C15
76) [61, 165, 4961] [1] 2 [61, 165, 4961] 30 C30
77) [17, 210, 2797] [1] 1 [17, 210, 2797] 15 C15
78) [17, 318, 18481] [1] 1 [17, 318, 18481] 15 C15
79) [17, 631, 85732] [1] 1 [17, 631, 85732] 15 C15
80) [17, 207, 10708] [1] 1 [17, 207, 10708] 15 C15
81) [17, 207, 10708] [2] 1 [17, 207, 10708] 15 C15
82) [17, 98, 1789] [1] 1 [17, 98, 1789] 15 C15
83) [17, 558, 31873] [1] 1 [17, 558, 31873] 15 C15
84) [373, 149, 981] [1] 1 [373, 149, 981] 15 C15
85) [773, 114, 157] [1] 1 [773, 114, 157] 15 C15
86) [2393, 51, 52] [1] 1 [2393, 51, 52] 15 C15
87) [3389, 245, 7381] [1] 1 [3389, 245, 7381] 15 C15
88) [569, 327, 2692] [1] 1 [569, 327, 2692] 15 C15
89) [44, 192, 9172] [1] 2 [44, 192, 9172] 30 C30
90) [44, 84, 1588] [1] 2 [44, 84, 1588] 30 C30
91) [12, 280, 7693] [1] 4 [12, 280, 7693] 60 C2 x C30
92) [12, 94, 1621] [1] 2 [12, 94, 1621] 30 C30
93) [101, 125, 1861] [1] 1 [101, 125, 1861] 15 C15
94) [101, 215, 421] [1] 2 [101, 215, 421] 30 C30
95) [2297, 311, 19012] [1] 1 [2297, 311, 19012] 15 C15