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 100 Igusa CM invariants of non-normal (D4) fields: 180

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [1893, 853, 45133] [1] 1 [1893, 853, 45133] 50 C50
2) [2429, 645, 1381] [1] 1 [2429, 645, 1381] 150 C150
3) [1529, 959, 61348] [1] 2 [1529, 959, 61348] 100 C2 x C50
4) [237, 137, 4633] [1] 1 [237, 137, 4633] 50 C50
5) [60, 664, 72724] [1] 2 [60, 664, 72724] 200 C2 x C100
6) [60, 214, 10909] [1] 2 [60, 214, 10909] 200 C2 x C100
7) [584, 930, 5401] [1] 1 [584, 930, 5401] 100 C100
8) [409, 355, 1956] [1] 1 [409, 355, 1956] 50 C50
9) [236, 754, 6193] [1] 1 [236, 754, 6193] 50 C50
10) [376, 244, 1348] [1] 2 [376, 244, 1348] 100 C2 x C50
11) [3737, 75, 472] [1] 1 [3737, 75, 472] 100 C100
12) [88, 292, 18148] [1] 2 [88, 292, 18148] 100 C2 x C50
13) [1937, 966, 231352] [1] 1 [1937, 966, 231352] 300 C300
14) [104, 186, 7713] [1] 2 [104, 186, 7713] 200 C2 x C10 x C10
15) [104, 228, 2596] [1] 1 [104, 228, 2596] 100 C100
16) [161, 1135, 260836] [1] 1 [161, 1135, 260836] 50 C50
17) [161, 162, 5917] [1] 1 [161, 162, 5917] 50 C50
18) [109, 177, 6497] [1] 1 [109, 177, 6497] 50 C50
19) [97, 595, 25432] [1] 2 [97, 595, 25432] 100 C2 x C50
20) [57, 1231, 359332] [1] 1 [57, 1231, 359332] 50 C50
21) [348, 70, 877] [1] 2 [348, 70, 877] 200 C10 x C20
22) [205, 129, 1649] [1] 1 [205, 129, 1649] 100 C100
23) [253, 129, 4097] [1] 1 [253, 129, 4097] 50 C50
24) [377, 237, 2638] [1] 1 [377, 237, 2638] 100 C100
25) [217, 823, 28228] [1] 1 [217, 823, 28228] 50 C5 x C10
26) [13, 438, 27161] [1] 1 [13, 438, 27161] 50 C50
27) [76, 102, 2297] [1] 1 [76, 102, 2297] 50 C50
28) [76, 34, 118] [1] 1 [76, 34, 118] 50 C50
29) [8, 906, 204409] [1] 2 [8, 906, 204409] 100 C2 x C50
30) [8, 666, 98089] [1] 2 [8, 666, 98089] 100 C2 x C50
31) [8, 994, 202009] [1] 1 [8, 994, 202009] 50 C50
32) [8, 1266, 399337] [1] 1 [8, 1266, 399337] 50 C50
33) [8, 1362, 416329] [1] 1 [8, 1362, 416329] 50 C50
34) [8, 1110, 160057] [1] 1 [8, 1110, 160057] 50 C50
35) [8, 934, 218017] [1] 2 [8, 934, 218017] 100 C2 x C50
36) [8, 1830, 834025] [1] 2 [8, 1830, 834025] 100 C2 x C50
37) [8, 870, 188833] [1] 2 [8, 870, 188833] 100 C5 x C20
38) [8, 442, 48553] [1] 2 [8, 442, 48553] 100 C2 x C50
39) [8, 1106, 196297] [1] 1 [8, 1106, 196297] 50 C50
40) [8, 168, 5806] [1] 1 [8, 168, 5806] 50 C50
41) [8, 1078, 186553] [1] 1 [8, 1078, 186553] 50 C50
42) [8, 758, 140113] [1] 2 [8, 758, 140113] 100 C10 x C10
43) [8, 822, 163921] [1] 2 [8, 822, 163921] 100 C2 x C50
44) [8, 192, 9166] [1] 1 [8, 192, 9166] 50 C50
45) [8, 554, 69529] [1] 2 [8, 554, 69529] 100 C2 x C50
46) [8, 714, 126937] [1] 2 [8, 714, 126937] 100 C10 x C10
47) [5, 283, 19921] [1] 2 [5, 283, 19921] 100 C2 x C50
48) [5, 181, 7409] [5, 5] 1 [5, 181, 7409] 10 C10
49) [5, 348, 28996] [1] 2 [5, 348, 28996] 100 C10 x C10
50) [5, 1137, 262141] [1] 1 [5, 1137, 262141] 50 C5 x C10
51) [5, 282, 15961] [1] 2 [5, 282, 15961] 100 C2 x C50
52) [5, 753, 140701] [1] 1 [5, 753, 140701] 50 C50
53) [5, 1397, 486541] [1] 2 [5, 1397, 486541] 100 C2 x C50
54) [5, 601, 79489] [1] 1 [5, 601, 79489] 50 C5 x C10
55) [5, 323, 21121] [1] 2 [5, 323, 21121] 100 C100
56) [5, 841, 149809] [1] 1 [5, 841, 149809] 50 C50
57) [5, 1253, 325801] [1] 2 [5, 1253, 325801] 100 C2 x C50
58) [5, 502, 60121] [1] 1 [5, 502, 60121] 50 C50
59) [5, 1201, 290389] [1] 1 [5, 1201, 290389] 50 C50
60) [5, 1601, 628549] [1] 1 [5, 1601, 628549] 50 C50
61) [5, 363, 32881] [1] 2 [5, 363, 32881] 100 C2 x C50
62) [5, 806, 161129] [1] 1 [5, 806, 161129] 50 C50
63) [5, 404, 40084] [1] 2 [5, 404, 40084] 100 C10 x C10
64) [5, 898, 171181] [1] 1 [5, 898, 171181] 50 C50
65) [5, 1269, 364309] [1] 1 [5, 1269, 364309] 50 C5 x C10
66) [5, 1369, 461509] [1] 1 [5, 1369, 461509] 50 C50
67) [5, 1341, 373309] [1] 1 [5, 1341, 373309] 50 C50
68) [5, 1326, 416449] [1] 2 [5, 1326, 416449] 100 C10 x C10
69) [5, 1401, 439189] [1] 1 [5, 1401, 439189] 50 C5 x C10
70) [5, 166, 5609] [5, 5] 1 [5, 166, 5609] 10 C10
71) [5, 997, 227701] [1] 1 [5, 997, 227701] 50 C50
72) [5, 1121, 266629] [1] 1 [5, 1121, 266629] 50 C50
73) [5, 513, 62281] [1] 1 [5, 513, 62281] 50 C50
74) [5, 428, 45076] [1] 2 [5, 428, 45076] 100 C2 x C50
75) [5, 459, 52609] [1] 2 [5, 459, 52609] 100 C100
76) [5, 818, 152701] [1] 1 [5, 818, 152701] 50 C50
77) [29, 486, 47449] [1] 1 [29, 486, 47449] 50 C50
78) [29, 1161, 184549] [1] 1 [29, 1161, 184549] 50 C50
79) [29, 300, 15076] [1] 2 [29, 300, 15076] 100 C5 x C20
80) [92, 92, 1909] [1] 2 [92, 92, 1909] 100 C2 x C50
81) [92, 108, 2893] [1] 2 [92, 108, 2893] 100 C10 x C10
82) [193, 895, 43492] [1] 1 [193, 895, 43492] 50 C50
83) [124, 994, 28273] [1] 2 [124, 994, 28273] 100 C2 x C50
84) [905, 33, 46] [1] 1 [905, 33, 46] 200 C200
85) [93, 209, 10897] [1] 1 [93, 209, 10897] 50 C5 x C10
86) [2501, 681, 100309] [1] 1 [2501, 681, 100309] 200 C5 x C40
87) [24, 190, 8161] [1] 1 [24, 190, 8161] 50 C50
88) [24, 1156, 216484] [1] 2 [24, 1156, 216484] 100 C2 x C50
89) [24, 178, 5521] [1] 2 [24, 178, 5521] 100 C2 x C50
90) [24, 382, 13417] [1] 2 [24, 382, 13417] 100 C2 x C50
91) [221, 513, 49825] [1] 1 [221, 513, 49825] 100 C100
92) [893, 39, 157] [1] 2 [893, 39, 157] 100 C2 x C50
93) [428, 60, 472] [1] 1 [428, 60, 472] 50 C50
94) [40, 886, 22009] [1] 1 [40, 886, 22009] 100 C100
95) [40, 186, 7649] [1] 1 [40, 186, 7649] 100 C10 x C10
96) [40, 466, 25129] [1] 1 [40, 466, 25129] 100 C100
97) [40, 178, 2161] [1] 2 [40, 178, 2161] 200 C2 x C100
98) [40, 274, 13009] [1] 2 [40, 274, 13009] 200 C2 x C100
99) [40, 138, 2801] [1] 1 [40, 138, 2801] 100 C2 x C50
100) [149, 961, 21349] [1] 1 [149, 961, 21349] 50 C50
101) [140, 976, 25204] [1] 2 [140, 976, 25204] 200 C2 x C100
102) [140, 188, 3796] [1] 2 [140, 188, 3796] 200 C2 x C100
103) [140, 192, 5716] [1] 2 [140, 192, 5716] 200 C10 x C20
104) [113, 1015, 43732] [1] 2 [113, 1015, 43732] 100 C100
105) [113, 1127, 274564] [1] 1 [113, 1127, 274564] 50 C50
106) [185, 114, 2509] [1] 1 [185, 114, 2509] 100 C100
107) [185, 178, 1261] [1] 1 [185, 178, 1261] 100 C100
108) [89, 966, 90889] [1] 1 [89, 966, 90889] 50 C50
109) [305, 951, 97924] [1] 1 [305, 951, 97924] 100 C100
110) [53, 1070, 95425] [1] 2 [53, 1070, 95425] 100 C2 x C50
111) [53, 229, 13097] [1] 1 [53, 229, 13097] 50 C50
112) [332, 62, 214] [1] 1 [332, 62, 214] 50 C50
113) [2833, 487, 1924] [1] 1 [2833, 487, 1924] 50 C50
114) [785, 89, 214] [1] 1 [785, 89, 214] 300 C300
115) [28, 262, 4813] [1] 2 [28, 262, 4813] 100 C100
116) [28, 202, 3901] [1] 2 [28, 202, 3901] 100 C2 x C50
117) [28, 268, 8884] [1] 2 [28, 268, 8884] 100 C100
118) [412, 350, 30213] [1] 2 [412, 350, 30213] 100 C100
119) [1249, 293, 21150] [1] 1 [1249, 293, 21150] 50 C50
120) [17, 1158, 203593] [1] 1 [17, 1158, 203593] 50 C50
121) [17, 1126, 160297] [1] 1 [17, 1126, 160297] 50 C50
122) [17, 995, 238900] [1] 2 [17, 995, 238900] 100 C5 x C20
123) [17, 299, 22244] [1] 1 [17, 299, 22244] 50 C50
124) [17, 1727, 744676] [1] 1 [17, 1727, 744676] 50 C50
125) [17, 915, 208792] [1] 1 [17, 915, 208792] 50 C50
126) [17, 252, 9076] [1] 2 [17, 252, 9076] 100 C2 x C50
127) [17, 1515, 568600] [1] 2 [17, 1515, 568600] 100 C2 x C50
128) [17, 450, 50557] [1] 1 [17, 450, 50557] 50 C50
129) [17, 1255, 346900] [1] 2 [17, 1255, 346900] 100 C100
130) [1868, 1002, 243529] [1] 1 [1868, 1002, 243529] 50 C50
131) [1112, 802, 673] [1] 2 [1112, 802, 673] 100 C10 x C10
132) [1112, 990, 110473] [1] 2 [1112, 990, 110473] 100 C2 x C50
133) [77, 193, 8369] [1] 1 [77, 193, 8369] 50 C50
134) [77, 260, 5812] [1] 2 [77, 260, 5812] 100 C2 x C50
135) [77, 985, 30325] [1] 2 [77, 985, 30325] 100 C2 x C50
136) [77, 282, 12181] [1] 1 [77, 282, 12181] 50 C5 x C10
137) [77, 897, 119821] [1] 2 [77, 897, 119821] 100 C10 x C10
138) [77, 213, 11169] [1] 2 [77, 213, 11169] 100 C2 x C50
139) [188, 422, 17449] [1] 1 [188, 422, 17449] 50 C5 x C10
140) [44, 946, 65329] [1] 1 [44, 946, 65329] 50 C50
141) [44, 286, 20053] [1] 2 [44, 286, 20053] 100 C10 x C10
142) [44, 70, 1126] [1] 1 [44, 70, 1126] 50 C5 x C10
143) [44, 1106, 147409] [1] 1 [44, 1106, 147409] 50 C50
144) [337, 403, 3448] [1] 1 [337, 403, 3448] 50 C50
145) [1292, 734, 30037] [1] 2 [1292, 734, 30037] 400 C2 x C200
146) [12, 622, 63013] [1] 2 [12, 622, 63013] 100 C2 x C50
147) [12, 178, 7489] [1] 1 [12, 178, 7489] 50 C50
148) [12, 418, 37333] [1] 2 [12, 418, 37333] 100 C10 x C10
149) [12, 430, 46117] [1] 2 [12, 430, 46117] 100 C2 x C50
150) [12, 238, 7249] [1] 1 [12, 238, 7249] 50 C50
151) [21, 649, 74173] [1] 2 [21, 649, 74173] 100 C2 x C50
152) [21, 529, 55213] [1] 1 [21, 529, 55213] 50 C50
153) [21, 925, 126541] [1] 1 [21, 925, 126541] 50 C50
154) [21, 409, 12289] [1] 1 [21, 409, 12289] 50 C50
155) [21, 244, 6484] [1] 2 [21, 244, 6484] 100 C10 x C10
156) [21, 745, 34381] [1] 1 [21, 745, 34381] 50 C5 x C10
157) [85, 153, 3281] [1] 1 [85, 153, 3281] 100 C100
158) [277, 605, 24957] [1] 1 [277, 605, 24957] 50 C50
159) [73, 895, 163300] [1] 2 [73, 895, 163300] 100 C2 x C50
160) [56, 564, 68548] [1] 2 [56, 564, 68548] 100 C10 x C10
161) [56, 554, 52033] [1] 1 [56, 554, 52033] 50 C50
162) [56, 570, 78481] [1] 1 [56, 570, 78481] 50 C50
163) [41, 1166, 192289] [1] 1 [41, 1166, 192289] 50 C50
164) [41, 519, 38548] [1] 1 [41, 519, 38548] 50 C50
165) [41, 354, 27229] [1] 1 [41, 354, 27229] 50 C50
166) [201, 82, 877] [1] 1 [201, 82, 877] 50 C50
167) [241, 187, 7236] [1] 1 [241, 187, 7236] 50 C50
168) [1961, 923, 173272] [1] 1 [1961, 923, 173272] 100 C100
169) [397, 57, 713] [1] 1 [397, 57, 713] 50 C50
170) [284, 68, 517] [1] 2 [284, 68, 517] 100 C10 x C10
171) [365, 909, 191149] [1] 1 [365, 909, 191149] 100 C5 x C20
172) [101, 181, 6953] [1] 1 [101, 181, 6953] 50 C50
173) [101, 693, 59437] [1] 2 [101, 693, 59437] 100 C100
174) [3521, 183, 7492] [1] 1 [3521, 183, 7492] 50 C50
175) [481, 205, 766] [1] 1 [481, 205, 766] 100 C100
176) [265, 61, 334] [1] 1 [265, 61, 334] 100 C100
177) [69, 221, 12193] [1] 1 [69, 221, 12193] 50 C50
178) [488, 806, 4297] [1] 1 [488, 806, 4297] 100 C2 x C50
179) [65, 306, 16909] [1] 1 [65, 306, 16909] 100 C100
180) [65, 1431, 496324] [1] 1 [65, 1431, 496324] 100 C100