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 42 Igusa CM invariants of non-normal (D4) fields: 71

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 382, 31409] [1] 1 [317, 382, 31409] 21 C21
2) [317, 57, 733] [1] 1 [317, 57, 733] 21 C21
3) [137, 135, 3700] [2] 2 [137, 135, 3700] 42 C42
4) [137, 135, 3700] [1] 2 [137, 135, 3700] 42 C42
5) [109, 518, 4297] [1] 1 [109, 518, 4297] 21 C21
6) [797, 481, 257] [1] 1 [797, 481, 257] 21 C21
7) [1709, 169, 6713] [1] 1 [1709, 169, 6713] 21 C21
8) [13, 333, 23273] [1] 2 [13, 333, 23273] 42 C42
9) [13, 118, 1609] [1] 1 [13, 118, 1609] 21 C21
10) [13, 437, 15889] [1] 1 [13, 437, 15889] 21 C21
11) [13, 118, 1609] [2, 2] 1 [13, 118, 1609] 21 C21
12) [13, 485, 30697] [1] 1 [13, 485, 30697] 21 C21
13) [13, 157, 6133] [1] 1 [13, 157, 6133] 21 C21
14) [76, 160, 5716] [1] 2 [76, 160, 5716] 42 C42
15) [8, 306, 22441] [1] 1 [8, 306, 22441] 21 C21
16) [8, 434, 45289] [1] 1 [8, 434, 45289] 21 C21
17) [8, 486, 50857] [1] 1 [8, 486, 50857] 21 C21
18) [8, 570, 79425] [1] 4 [8, 570, 79425] 84 C2 x C42
19) [5, 889, 197029] [1] 2 [5, 889, 197029] 42 C42
20) [5, 286, 17569] [1] 1 [5, 286, 17569] 21 C21
21) [5, 198, 9721] [1] 1 [5, 198, 9721] 21 C21
22) [5, 321, 24049] [1] 1 [5, 321, 24049] 21 C21
23) [5, 609, 88069] [1] 1 [5, 609, 88069] 21 C21
24) [5, 259, 14869] [1] 2 [5, 259, 14869] 42 C42
25) [5, 629, 90709] [1] 1 [5, 629, 90709] 21 C21
26) [5, 409, 40289] [1] 1 [5, 409, 40289] 21 C21
27) [5, 334, 27809] [1] 1 [5, 334, 27809] 21 C21
28) [5, 501, 54949] [1] 1 [5, 501, 54949] 21 C21
29) [5, 333, 25621] [1] 1 [5, 333, 25621] 21 C21
30) [5, 586, 77029] [1] 1 [5, 586, 77029] 21 C21
31) [5, 361, 32369] [1] 1 [5, 361, 32369] 21 C21
32) [5, 261, 16249] [1] 1 [5, 261, 16249] 21 C21
33) [5, 714, 125029] [1] 1 [5, 714, 125029] 21 C21
34) [5, 661, 108949] [1] 1 [5, 661, 108949] 21 C21
35) [5, 449, 46889] [1] 1 [5, 449, 46889] 21 C21
36) [5, 198, 9721] [2, 2] 1 [5, 198, 9721] 21 C21
37) [5, 249, 15289] [1] 1 [5, 249, 15289] 21 C21
38) [5, 801, 129589] [1] 1 [5, 801, 129589] 21 C21
39) [5, 446, 48449] [1] 1 [5, 446, 48449] 21 C21
40) [5, 269, 18089] [1] 1 [5, 269, 18089] 21 C21
41) [5, 549, 74149] [1] 1 [5, 549, 74149] 21 C21
42) [5, 666, 98389] [1] 1 [5, 666, 98389] 21 C21
43) [5, 177, 7681] [1] 1 [5, 177, 7681] 21 C21
44) [5, 294, 21529] [1] 1 [5, 294, 21529] 21 C21
45) [5, 454, 47609] [1] 1 [5, 454, 47609] 21 C21
46) [29, 430, 8641] [1] 1 [29, 430, 8641] 21 C21
47) [29, 126, 2113] [2, 2] 1 [29, 126, 2113] 21 C21
48) [29, 126, 2113] [1] 1 [29, 126, 2113] 21 C21
49) [1637, 1050, 111925] [1] 2 [1637, 1050, 111925] 42 C42
50) [149, 129, 3229] [1] 1 [149, 129, 3229] 21 C21
51) [149, 117, 1597] [1] 1 [149, 117, 1597] 21 C21
52) [1453, 237, 4961] [1] 1 [1453, 237, 4961] 21 C21
53) [113, 299, 22096] [1] 1 [113, 299, 22096] 21 C21
54) [1229, 41, 113] [1] 1 [1229, 41, 113] 63 C3 x C21
55) [53, 313, 6353] [1] 1 [53, 313, 6353] 21 C21
56) [37, 237, 5153] [1] 1 [37, 237, 5153] 21 C21
57) [37, 126, 1601] [1] 1 [37, 126, 1601] 21 C21
58) [37, 31, 157] [1] 2 [37, 31, 157] 42 C42
59) [293, 69, 1117] [1] 1 [293, 69, 1117] 21 C21
60) [293, 329, 617] [1] 1 [293, 329, 617] 21 C21
61) [197, 133, 433] [1] 1 [197, 133, 433] 21 C21
62) [197, 566, 1289] [1] 1 [197, 566, 1289] 21 C21
63) [173, 285, 4693] [1] 2 [173, 285, 4693] 42 C42
64) [1429, 305, 20041] [1] 1 [1429, 305, 20041] 105 C105
65) [12, 136, 1741] [1] 2 [12, 136, 1741] 42 C42
66) [277, 393, 30233] [1] 1 [277, 393, 30233] 21 C21
67) [73, 175, 7492] [1] 1 [73, 175, 7492] 21 C21
68) [1609, 59, 468] [1] 1 [1609, 59, 468] 21 C21
69) [353, 1011, 181312] [1] 1 [353, 1011, 181312] 21 C21
70) [101, 429, 18513] [1] 4 [101, 429, 18513] 84 C2 x C42
71) [557, 77, 229] [1] 1 [557, 77, 229] 21 C21