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 252 Igusa CM invariants of non-normal (D4) fields: 97

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [661, 581, 47209] [1] 1 [661, 581, 47209] 126 C126
2) [1853, 97, 1889] [1] 1 [1853, 97, 1889] 252 C2 x C126
3) [237, 518, 51913] [1] 1 [237, 518, 51913] 126 C126
4) [1237, 365, 8257] [1] 1 [1237, 365, 8257] 126 C3 x C42
5) [229, 765, 129761] [1] 2 [229, 765, 129761] 756 C6 x C126
6) [301, 653, 73417] [1] 1 [301, 653, 73417] 126 C126
7) [236, 454, 5273] [1] 1 [236, 454, 5273] 126 C126
8) [88, 318, 23873] [1] 1 [88, 318, 23873] 126 C126
9) [88, 402, 14969] [1] 1 [88, 402, 14969] 126 C126
10) [461, 681, 90009] [1] 2 [461, 681, 90009] 252 C2 x C126
11) [213, 653, 78433] [1] 1 [213, 653, 78433] 126 C126
12) [109, 509, 52753] [1] 1 [109, 509, 52753] 126 C126
13) [797, 513, 20961] [1] 2 [797, 513, 20961] 252 C2 x C126
14) [205, 701, 100249] [1] 1 [205, 701, 100249] 252 C252
15) [309, 605, 50641] [1] 1 [309, 605, 50641] 126 C126
16) [1765, 141, 4529] [1] 1 [1765, 141, 4529] 756 C3 x C252
17) [844, 474, 2153] [1] 1 [844, 474, 2153] 126 C126
18) [493, 557, 23209] [1] 1 [493, 557, 23209] 252 C2 x C126
19) [493, 665, 82825] [1] 2 [493, 665, 82825] 504 C2 x C2 x C126
20) [13, 1862, 597193] [1] 1 [13, 1862, 597193] 126 C126
21) [13, 1446, 392729] [1] 1 [13, 1446, 392729] 126 C126
22) [13, 2294, 566809] [1] 1 [13, 2294, 566809] 126 C126
23) [13, 2414, 1426897] [1] 1 [13, 2414, 1426897] 126 C126
24) [13, 2294, 948697] [1] 1 [13, 2294, 948697] 126 C126
25) [76, 534, 19913] [1] 1 [76, 534, 19913] 126 C126
26) [8, 878, 192433] [1] 1 [8, 878, 192433] 126 C126
27) [8, 1546, 472529] [1] 1 [8, 1546, 472529] 126 C126
28) [8, 970, 153617] [1] 1 [8, 970, 153617] 126 C126
29) [5, 3181, 2518409] [1] 1 [5, 3181, 2518409] 126 C126
30) [5, 1657, 679001] [1] 1 [5, 1657, 679001] 126 C126
31) [5, 1981, 975809] [1] 1 [5, 1981, 975809] 126 C126
32) [5, 1981, 954809] [1] 1 [5, 1981, 954809] 126 C126
33) [5, 1342, 442241] [1] 1 [5, 1342, 442241] 126 C126
34) [5, 2461, 1313129] [1] 1 [5, 2461, 1313129] 126 C126
35) [5, 2806, 1576409] [1] 1 [5, 2806, 1576409] 126 C126
36) [29, 809, 152593] [1] 1 [29, 809, 152593] 126 C126
37) [29, 697, 116921] [1] 1 [29, 697, 116921] 126 C126
38) [93, 605, 91297] [1] 1 [93, 605, 91297] 126 C126
39) [93, 593, 82681] [1] 1 [93, 593, 82681] 126 C126
40) [93, 710, 102217] [1] 1 [93, 710, 102217] 126 C126
41) [24, 734, 115873] [1] 1 [24, 734, 115873] 126 C126
42) [24, 926, 211969] [1] 1 [24, 926, 211969] 126 C126
43) [221, 550, 61481] [1] 1 [221, 550, 61481] 252 C252
44) [1141, 393, 4097] [1] 1 [1141, 393, 4097] 126 C126
45) [141, 614, 58153] [1] 1 [141, 614, 58153] 126 C126
46) [1816, 114, 1433] [1] 1 [1816, 114, 1433] 126 C126
47) [40, 794, 148609] [1] 1 [40, 794, 148609] 252 C2 x C126
48) [40, 986, 242689] [1] 1 [40, 986, 242689] 252 C2 x C126
49) [40, 606, 60449] [1] 1 [40, 606, 60449] 252 C2 x C126
50) [149, 529, 38633] [1] 1 [149, 529, 38633] 126 C126
51) [1832, 106, 977] [1] 1 [1832, 106, 977] 252 C2 x C126
52) [533, 537, 13329] [1] 2 [533, 537, 13329] 504 C2 x C2 x C126
53) [53, 605, 48457] [1] 1 [53, 605, 48457] 126 C126
54) [53, 733, 127313] [1] 1 [53, 733, 127313] 126 C126
55) [53, 853, 178073] [1] 1 [53, 853, 178073] 126 C126
56) [1189, 389, 13753] [1] 1 [1189, 389, 13753] 252 C252
57) [37, 558, 48833] [1] 1 [37, 558, 48833] 126 C126
58) [37, 726, 131177] [1] 1 [37, 726, 131177] 126 C126
59) [1477, 281, 16417] [1] 1 [1477, 281, 16417] 126 C126
60) [293, 305, 14393] [1] 1 [293, 305, 14393] 126 C126
61) [197, 505, 22337] [1] 1 [197, 505, 22337] 126 C126
62) [173, 245, 14617] [1] 1 [173, 245, 14617] 126 C126
63) [173, 365, 28073] [1] 1 [173, 365, 28073] 126 C3 x C42
64) [1676, 178, 1217] [1] 1 [1676, 178, 1217] 126 C126
65) [133, 737, 121129] [1] 1 [133, 737, 121129] 126 C126
66) [133, 593, 63673] [1] 1 [133, 593, 63673] 126 C126
67) [1261, 353, 5617] [1] 1 [1261, 353, 5617] 252 C252
68) [1165, 401, 16609] [1] 1 [1165, 401, 16609] 252 C252
69) [77, 673, 101201] [1] 1 [77, 673, 101201] 126 C126
70) [77, 673, 111673] [1] 1 [77, 673, 111673] 126 C126
71) [44, 714, 121113] [1] 2 [44, 714, 121113] 252 C2 x C126
72) [44, 654, 100593] [1] 2 [44, 654, 100593] 252 C2 x C126
73) [12, 730, 131497] [1] 1 [12, 730, 131497] 126 C126
74) [12, 806, 161977] [1] 1 [12, 806, 161977] 126 C126
75) [12, 1010, 254977] [1] 1 [12, 1010, 254977] 126 C126
76) [12, 878, 187921] [1] 1 [12, 878, 187921] 126 C126
77) [12, 962, 230929] [1] 1 [12, 962, 230929] 126 C126
78) [12, 562, 57793] [1] 1 [12, 562, 57793] 126 C126
79) [12, 902, 201049] [1] 1 [12, 902, 201049] 126 C126
80) [12, 622, 89809] [1] 1 [12, 622, 89809] 126 C126
81) [12, 938, 218233] [1] 1 [12, 938, 218233] 126 C126
82) [21, 1013, 256537] [1] 1 [21, 1013, 256537] 126 C126
83) [21, 737, 129361] [1] 1 [21, 737, 129361] 126 C126
84) [21, 694, 93193] [1] 1 [21, 694, 93193] 126 C126
85) [21, 929, 215713] [1] 1 [21, 929, 215713] 126 C126
86) [21, 782, 144481] [1] 1 [21, 782, 144481] 126 C126
87) [85, 782, 140641] [1] 1 [85, 782, 140641] 252 C252
88) [85, 726, 110009] [1] 1 [85, 726, 110009] 252 C252
89) [85, 941, 219649] [1] 1 [85, 941, 219649] 252 C2 x C126
90) [1349, 325, 9881] [1] 1 [1349, 325, 9881] 126 C126
91) [365, 529, 12929] [1] 1 [365, 529, 12929] 252 C252
92) [381, 569, 30553] [1] 1 [381, 569, 30553] 126 C126
93) [69, 629, 72673] [1] 1 [69, 629, 72673] 126 C3 x C42
94) [69, 625, 85081] [1] 1 [69, 625, 85081] 126 C126
95) [69, 601, 55369] [1] 1 [69, 601, 55369] 126 C126
96) [69, 965, 231961] [1] 1 [69, 965, 231961] 126 C126
97) [65, 606, 54369] [1] 2 [65, 606, 54369] 504 C2 x C252