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 280 Igusa CM invariants of non-normal (D4) fields: 127

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [165, 574, 16369] [1] 1 [165, 574, 16369] 280 C2 x C2 x C70
2) [344, 1014, 90553] [1] 1 [344, 1014, 90553] 140 C140
3) [157, 833, 164641] [1] 1 [157, 833, 164641] 140 C2 x C70
4) [237, 593, 50881] [1] 1 [237, 593, 50881] 140 C2 x C70
5) [1117, 425, 22537] [1] 1 [1117, 425, 22537] 140 C140
6) [437, 541, 15377] [1] 1 [437, 541, 15377] 140 C140
7) [60, 566, 39529] [1] 1 [60, 566, 39529] 280 C2 x C140
8) [60, 626, 63409] [1] 1 [60, 626, 63409] 280 C2 x C2 x C70
9) [60, 866, 183649] [1] 1 [60, 866, 183649] 280 C2 x C140
10) [60, 662, 80521] [1] 1 [60, 662, 80521] 280 C2 x C140
11) [885, 469, 5209] [1] 1 [885, 469, 5209] 280 C2 x C140
12) [229, 421, 31429] [1] 1 [229, 421, 31429] 420 C420
13) [301, 561, 31649] [1] 1 [301, 561, 31649] 140 C140
14) [805, 509, 19489] [1] 1 [805, 509, 19489] 280 C2 x C2 x C70
15) [137, 1035, 210232] [1] 1 [137, 1035, 210232] 140 C2 x C70
16) [88, 530, 31417] [1] 1 [88, 530, 31417] 140 C2 x C70
17) [120, 542, 15361] [1] 1 [120, 542, 15361] 280 C2 x C2 x C70
18) [120, 178, 6841] [1] 1 [120, 178, 6841] 280 C2 x C2 x C70
19) [665, 1247, 267556] [1] 1 [665, 1247, 267556] 280 C2 x C140
20) [665, 582, 42121] [1] 1 [665, 582, 42121] 280 C2 x C140
21) [357, 302, 17089] [1] 1 [357, 302, 17089] 280 C2 x C140
22) [104, 574, 32033] [1] 1 [104, 574, 32033] 280 C2 x C2 x C70
23) [312, 530, 17497] [1] 1 [312, 530, 17497] 280 C2 x C2 x C70
24) [109, 965, 232561] [1] 1 [109, 965, 232561] 140 C140
25) [309, 398, 34657] [1] 1 [309, 398, 34657] 140 C140
26) [1501, 1189, 350053] [1] 1 [1501, 1189, 350053] 140 C140
27) [136, 186, 8513] [1] 1 [136, 186, 8513] 280 C2 x C140
28) [209, 1238, 262777] [1] 1 [209, 1238, 262777] 140 C140
29) [13, 601, 68977] [1] 1 [13, 601, 68977] 140 C140
30) [13, 993, 246353] [1] 1 [13, 993, 246353] 140 C140
31) [8, 874, 185969] [1] 1 [8, 874, 185969] 140 C2 x C70
32) [8, 826, 164737] [1] 1 [8, 826, 164737] 140 C140
33) [8, 862, 183169] [1] 1 [8, 862, 183169] 140 C2 x C70
34) [5, 1737, 743941] [1] 1 [5, 1737, 743941] 140 C140
35) [5, 1542, 555721] [1] 1 [5, 1542, 555721] 140 C140
36) [29, 629, 64393] [1] 1 [29, 629, 64393] 140 C140
37) [29, 1709, 726973] [1] 1 [29, 1709, 726973] 140 C140
38) [29, 749, 121393] [1] 1 [29, 749, 121393] 140 C140
39) [29, 577, 52601] [1] 1 [29, 577, 52601] 140 C140
40) [29, 893, 199297] [1] 1 [29, 893, 199297] 140 C2 x C70
41) [29, 829, 169193] [1] 1 [29, 829, 169193] 140 C140
42) [92, 1182, 242929] [1] 1 [92, 1182, 242929] 140 C140
43) [124, 458, 47977] [1] 1 [124, 458, 47977] 140 C140
44) [124, 534, 11273] [1] 1 [124, 534, 11273] 140 C140
45) [124, 730, 61801] [1] 1 [124, 730, 61801] 140 C2 x C70
46) [124, 614, 54073] [1] 1 [124, 614, 54073] 140 C2 x C70
47) [124, 450, 18881] [1] 1 [124, 450, 18881] 140 C2 x C70
48) [93, 893, 195433] [1] 1 [93, 893, 195433] 140 C140
49) [93, 565, 62857] [1] 1 [93, 565, 62857] 140 C2 x C70
50) [93, 493, 13681] [1] 1 [93, 493, 13681] 140 C140
51) [93, 550, 22057] [1] 1 [93, 550, 22057] 140 C2 x C70
52) [24, 670, 81121] [1] 1 [24, 670, 81121] 140 C2 x C70
53) [24, 1690, 711121] [1] 1 [24, 1690, 711121] 140 C140
54) [24, 418, 33097] [1] 1 [24, 418, 33097] 140 C2 x C70
55) [24, 818, 156697] [1] 1 [24, 818, 156697] 140 C2 x C70
56) [24, 734, 123073] [1] 1 [24, 734, 123073] 140 C2 x C70
57) [24, 674, 109513] [1] 1 [24, 674, 109513] 140 C2 x C70
58) [24, 922, 163921] [1] 1 [24, 922, 163921] 140 C2 x C70
59) [221, 601, 55769] [1] 1 [221, 601, 55769] 280 C2 x C140
60) [1549, 245, 11521] [1] 1 [1549, 245, 11521] 140 C140
61) [285, 422, 26281] [1] 1 [285, 422, 26281] 280 C2 x C2 x C70
62) [285, 446, 45169] [1] 1 [285, 446, 45169] 280 C2 x C140
63) [105, 619, 79384] [1] 1 [105, 619, 79384] 280 C2 x C140
64) [141, 710, 117001] [1] 1 [141, 710, 117001] 140 C2 x C70
65) [141, 769, 69973] [1] 1 [141, 769, 69973] 140 C2 x C70
66) [152, 322, 13609] [1] 1 [152, 322, 13609] 140 C2 x C70
67) [40, 842, 176881] [1] 1 [40, 842, 176881] 280 C2 x C2 x C70
68) [40, 926, 212929] [1] 1 [40, 926, 212929] 280 C2 x C2 x C70
69) [185, 1062, 92521] [1] 1 [185, 1062, 92521] 280 C2 x C140
70) [185, 389, 37414] [1] 1 [185, 389, 37414] 280 C2 x C140
71) [156, 550, 25081] [1] 1 [156, 550, 25081] 280 C2 x C140
72) [53, 673, 86401] [1] 1 [53, 673, 86401] 140 C140
73) [957, 461, 12697] [1] 1 [957, 461, 12697] 280 C2 x C2 x C70
74) [37, 857, 183529] [1] 1 [37, 857, 183529] 140 C140
75) [37, 797, 148729] [1] 1 [37, 797, 148729] 140 C140
76) [789, 545, 40921] [1] 1 [789, 545, 40921] 140 C140
77) [364, 554, 24313] [1] 1 [364, 554, 24313] 280 C2 x C140
78) [28, 778, 115033] [1] 1 [28, 778, 115033] 140 C140
79) [28, 866, 183457] [1] 1 [28, 866, 183457] 140 C2 x C70
80) [28, 630, 80297] [1] 1 [28, 630, 80297] 140 C2 x C70
81) [28, 618, 89993] [1] 1 [28, 618, 89993] 140 C2 x C70
82) [28, 782, 148849] [1] 1 [28, 782, 148849] 140 C2 x C70
83) [28, 498, 54833] [1] 1 [28, 498, 54833] 140 C140
84) [204, 530, 30241] [1] 1 [204, 530, 30241] 280 C2 x C2 x C70
85) [33, 1447, 488596] [1] 1 [33, 1447, 488596] 140 C140
86) [61, 953, 225817] [1] 1 [61, 953, 225817] 140 C140
87) [61, 397, 32677] [1] 1 [61, 397, 32677] 140 C140
88) [541, 641, 72289] [1] 1 [541, 641, 72289] 140 C2 x C70
89) [1101, 413, 9337] [1] 1 [1101, 413, 9337] 420 C420
90) [1085, 421, 11489] [1] 1 [1085, 421, 11489] 280 C2 x C140
91) [593, 963, 28888] [1] 1 [593, 963, 28888] 140 C2 x C70
92) [881, 1239, 267268] [1] 1 [881, 1239, 267268] 140 C140
93) [17, 478, 56033] [1] 1 [17, 478, 56033] 140 C140
94) [173, 521, 64357] [1] 1 [173, 521, 64357] 140 C140
95) [1644, 194, 2833] [1] 1 [1644, 194, 2833] 280 C2 x C2 x C70
96) [133, 385, 12817] [1] 1 [133, 385, 12817] 140 C140
97) [77, 721, 119777] [1] 1 [77, 721, 119777] 140 C2 x C70
98) [44, 442, 31241] [1] 1 [44, 442, 31241] 140 C2 x C70
99) [44, 1850, 854041] [1] 1 [44, 1850, 854041] 140 C140
100) [44, 970, 234521] [1] 1 [44, 970, 234521] 140 C2 x C70
101) [44, 886, 191849] [1] 1 [44, 886, 191849] 140 C2 x C70
102) [12, 758, 132841] [1] 1 [12, 758, 132841] 140 C2 x C70
103) [12, 1426, 492817] [1] 1 [12, 1426, 492817] 140 C2 x C70
104) [12, 998, 248953] [1] 1 [12, 998, 248953] 140 C2 x C70
105) [21, 925, 213481] [1] 1 [21, 925, 213481] 140 C140
106) [21, 1429, 470773] [1] 1 [21, 1429, 470773] 140 C2 x C70
107) [21, 677, 92401] [1] 1 [21, 677, 92401] 140 C140
108) [21, 1705, 713101] [1] 1 [21, 1705, 713101] 140 C2 x C70
109) [741, 509, 11233] [1] 1 [741, 509, 11233] 280 C2 x C140
110) [56, 610, 52201] [1] 1 [56, 610, 52201] 140 C140
111) [56, 418, 27497] [1] 1 [56, 418, 27497] 140 C2 x C70
112) [713, 510, 53617] [1] 1 [713, 510, 53617] 140 C140
113) [201, 1150, 173041] [1] 1 [201, 1150, 173041] 140 C2 x C70
114) [201, 739, 25528] [1] 1 [201, 739, 25528] 140 C2 x C70
115) [241, 811, 42424] [1] 1 [241, 811, 42424] 140 C140
116) [397, 222, 5969] [1] 1 [397, 222, 5969] 140 C140
117) [284, 406, 12809] [1] 1 [284, 406, 12809] 140 C140
118) [424, 714, 106673] [1] 1 [424, 714, 106673] 280 C2 x C2 x C70
119) [3009, 415, 6196] [1] 1 [3009, 415, 6196] 280 C2 x C2 x C70
120) [1133, 397, 5129] [1] 1 [1133, 397, 5129] 140 C140
121) [1356, 314, 2953] [1] 1 [1356, 314, 2953] 280 C2 x C2 x C70
122) [904, 522, 45521] [1] 1 [904, 522, 45521] 1120 C2 x C560
123) [69, 809, 157393] [1] 1 [69, 809, 157393] 140 C140
124) [69, 689, 111073] [1] 1 [69, 689, 111073] 140 C140
125) [69, 445, 30721] [1] 1 [69, 445, 30721] 140 C140
126) [69, 845, 173521] [1] 1 [69, 845, 173521] 140 C2 x C70
127) [1309, 365, 30361] [1] 1 [1309, 365, 30361] 280 C2 x C140