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 6 Igusa CM invariants of non-normal (D4) fields: 250

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [661, 29, 45] [1] 1 [661, 29, 45] 3 C3
2) [1117, 73, 1053] [1] 1 [1117, 73, 1053] 3 C3
3) [1117, 101, 37] [1] 1 [1117, 101, 37] 3 C3
4) [2857, 57, 98] [1] 1 [2857, 57, 98] 9 C3 x C3
5) [1361, 211, 2624] [1] 1 [1361, 211, 2624] 3 C3
6) [229, 27, 125] [1] 2 [229, 27, 125] 18 C3 x C6
7) [409, 27, 80] [1] 1 [409, 27, 80] 3 C3
8) [449, 206, 3425] [1] 1 [449, 206, 3425] 3 C3
9) [449, 23, 20] [1] 1 [449, 23, 20] 3 C3
10) [269, 61, 325] [1] 1 [269, 61, 325] 3 C3
11) [236, 62, 725] [1] 2 [236, 62, 725] 6 C6
12) [137, 103, 1796] [1] 1 [137, 103, 1796] 3 C3
13) [349, 23, 45] [1] 2 [349, 23, 45] 6 C6
14) [349, 57, 725] [1] 1 [349, 57, 725] 3 C3
15) [349, 145, 981] [1] 1 [349, 145, 981] 3 C3
16) [1069, 33, 5] [1] 1 [1069, 33, 5] 3 C3
17) [1033, 41, 162] [1] 1 [1033, 41, 162] 3 C3
18) [461, 93, 1125] [1] 2 [461, 93, 1125] 6 C6
19) [1049, 43, 200] [1] 1 [1049, 43, 200] 3 C3
20) [109, 161, 349] [1] 1 [109, 161, 349] 3 C3
21) [109, 35, 61] [1] 2 [109, 35, 61] 6 C6
22) [97, 39, 356] [1] 1 [97, 39, 356] 3 C3
23) [97, 13, 18] [1] 1 [97, 13, 18] 3 C3
24) [97, 65, 450] [1] 2 [97, 65, 450] 6 C6
25) [733, 154, 2997] [1] 1 [733, 154, 2997] 9 C3 x C3
26) [1516, 78, 5] [1] 2 [1516, 78, 5] 6 C6
27) [1433, 49, 242] [1] 1 [1433, 49, 242] 3 C3
28) [2269, 57, 245] [1] 1 [2269, 57, 245] 3 C3
29) [421, 21, 5] [1] 1 [421, 21, 5] 3 C3
30) [716, 58, 125] [1] 2 [716, 58, 125] 6 C6
31) [821, 29, 5] [1] 1 [821, 29, 5] 3 C3
32) [13, 9, 17] [2, 2] 1 [13, 9, 17] 1 C1
33) [13, 15, 53] [1] 2 [13, 15, 53] 6 C6
34) [13, 42, 389] [1] 1 [13, 42, 389] 3 C3
35) [13, 53, 673] [1] 1 [13, 53, 673] 3 C3
36) [13, 77, 1453] [1] 1 [13, 77, 1453] 3 C3
37) [13, 33, 269] [1] 1 [13, 33, 269] 3 C3
38) [13, 38, 244] [1] 2 [13, 38, 244] 6 C6
39) [13, 35, 277] [1] 2 [13, 35, 277] 6 C6
40) [13, 101, 1117] [1] 1 [13, 101, 1117] 3 C3
41) [13, 45, 425] [1] 2 [13, 45, 425] 6 C6
42) [13, 290, 9325] [1] 2 [13, 290, 9325] 6 C6
43) [13, 98, 1933] [1] 1 [13, 98, 1933] 3 C3
44) [13, 33, 113] [1] 1 [13, 33, 113] 3 C3
45) [13, 209, 7381] [1] 2 [13, 209, 7381] 6 C6
46) [76, 64, 549] [1] 2 [76, 64, 549] 6 C6
47) [76, 80, 916] [1] 2 [76, 80, 916] 6 C6
48) [76, 16, 45] [1] 2 [76, 16, 45] 6 C6
49) [76, 96, 404] [1] 2 [76, 96, 404] 6 C6
50) [8, 118, 2969] [1] 1 [8, 118, 2969] 3 C3
51) [8, 70, 937] [1] 1 [8, 70, 937] 3 C3
52) [8, 54, 601] [1] 1 [8, 54, 601] 3 C3
53) [8, 82, 1033] [1] 1 [8, 82, 1033] 3 C3
54) [8, 86, 1721] [1] 1 [8, 86, 1721] 3 C3
55) [8, 86, 1049] [1] 1 [8, 86, 1049] 3 C3
56) [8, 114, 3177] [1] 2 [8, 114, 3177] 6 C6
57) [8, 98, 2393] [1] 1 [8, 98, 2393] 3 C3
58) [8, 74, 857] [1] 2 [8, 74, 857] 6 C6
59) [8, 26, 97] [1] 1 [8, 26, 97] 3 C3
60) [8, 98, 1433] [1] 1 [8, 98, 1433] 3 C3
61) [8, 102, 2313] [1] 2 [8, 102, 2313] 6 C6
62) [8, 46, 521] [1] 2 [8, 46, 521] 6 C6
63) [8, 150, 4825] [1] 2 [8, 150, 4825] 6 C6
64) [8, 150, 5337] [1] 2 [8, 150, 5337] 6 C6
65) [8, 18, 73] [2] 1 [8, 18, 73] 1 C1
66) [8, 82, 1481] [1] 1 [8, 82, 1481] 3 C3
67) [8, 42, 313] [1] 2 [8, 42, 313] 6 C6
68) [8, 70, 1097] [1] 1 [8, 70, 1097] 3 C3
69) [8, 130, 2425] [1] 2 [8, 130, 2425] 6 C6
70) [8, 42, 409] [1] 2 [8, 42, 409] 6 C6
71) [8, 70, 1193] [1] 1 [8, 70, 1193] 3 C3
72) [8, 50, 617] [1] 1 [8, 50, 617] 3 C3
73) [8, 62, 953] [1] 2 [8, 62, 953] 6 C6
74) [8, 42, 369] [1] 2 [8, 42, 369] 6 C6
75) [8, 62, 761] [1] 2 [8, 62, 761] 6 C6
76) [8, 114, 2857] [1] 1 [8, 114, 2857] 3 C3
77) [556, 48, 20] [1] 2 [556, 48, 20] 6 C6
78) [556, 64, 468] [1] 2 [556, 64, 468] 6 C6
79) [5, 53, 701] [1] 1 [5, 53, 701] 3 C3
80) [5, 138, 4581] [1] 2 [5, 138, 4581] 6 C6
81) [5, 42, 421] [1] 1 [5, 42, 421] 3 C3
82) [5, 57, 801] [1] 2 [5, 57, 801] 6 C6
83) [5, 22, 116] [1] 2 [5, 22, 116] 6 C6
84) [5, 106, 2309] [1] 1 [5, 106, 2309] 3 C3
85) [5, 46, 509] [1] 2 [5, 46, 509] 6 C6
86) [5, 13, 41] [2, 2] 1 [5, 13, 41] 1 C1
87) [5, 73, 1181] [1] 1 [5, 73, 1181] 3 C3
88) [5, 154, 4949] [1] 2 [5, 154, 4949] 6 C6
89) [5, 58, 821] [1] 1 [5, 58, 821] 3 C3
90) [5, 101, 2269] [1] 1 [5, 101, 2269] 3 C3
91) [5, 66, 1069] [1] 1 [5, 66, 1069] 3 C3
92) [5, 39, 349] [1] 2 [5, 39, 349] 6 C6
93) [5, 106, 2789] [1] 1 [5, 106, 2789] 3 C3
94) [5, 61, 929] [1] 1 [5, 61, 929] 3 C3
95) [5, 49, 569] [1] 1 [5, 49, 569] 3 C3
96) [5, 22, 101] [1] 2 [5, 22, 101] 6 C6
97) [5, 41, 409] [1] 1 [5, 41, 409] 3 C3
98) [5, 37, 281] [1] 1 [5, 37, 281] 3 C3
99) [5, 33, 241] [2, 2] 1 [5, 33, 241] 3 C3
100) [5, 46, 449] [1] 1 [5, 46, 449] 3 C3
101) [5, 33, 241] [1] 1 [5, 33, 241] 3 C3
102) [5, 57, 661] [1] 1 [5, 57, 661] 3 C3
103) [5, 34, 244] [1] 2 [5, 34, 244] 6 C6
104) [5, 201, 9549] [1] 2 [5, 201, 9549] 6 C6
105) [5, 186, 8469] [1] 2 [5, 186, 8469] 6 C6
106) [5, 34, 244] [2, 2] 4 [5, 34, 244] 6 C6
107) [5, 101, 2549] [1] 1 [5, 101, 2549] 3 C3
108) [5, 61, 829] [1] 1 [5, 61, 829] 3 C3
109) [5, 129, 4149] [1] 2 [5, 129, 4149] 6 C6
110) [5, 81, 1429] [1] 1 [5, 81, 1429] 3 C3
111) [5, 41, 409] [2, 2] 1 [5, 41, 409] 3 C3
112) [5, 44, 404] [1] 2 [5, 44, 404] 6 C6
113) [5, 89, 1949] [1] 1 [5, 89, 1949] 3 C3
114) [5, 189, 8869] [1] 2 [5, 189, 8869] 6 C6
115) [5, 31, 229] [1] 2 [5, 31, 229] 6 C6
116) [5, 97, 1901] [1] 1 [5, 97, 1901] 3 C3
117) [29, 34, 173] [1] 1 [29, 34, 173] 3 C3
118) [29, 14, 20] [1] 2 [29, 14, 20] 6 C6
119) [29, 141, 1773] [1] 2 [29, 141, 1773] 6 C6
120) [29, 89, 349] [1] 1 [29, 89, 349] 3 C3
121) [29, 65, 701] [1] 1 [29, 65, 701] 3 C3
122) [941, 93, 45] [1] 2 [941, 93, 45] 6 C6
123) [193, 75, 200] [1] 2 [193, 75, 200] 6 C6
124) [193, 131, 3856] [1] 1 [193, 131, 3856] 3 C3
125) [1657, 107, 2448] [1] 1 [1657, 107, 2448] 3 C3
126) [1901, 49, 125] [1] 1 [1901, 49, 125] 9 C3 x C3
127) [257, 51, 72] [1] 2 [257, 51, 72] 18 C3 x C6
128) [401, 47, 452] [1] 1 [401, 47, 452] 15 C15
129) [313, 171, 7232] [1] 1 [313, 171, 7232] 3 C3
130) [1453, 125, 637] [1] 1 [1453, 125, 637] 3 C3
131) [509, 23, 5] [1] 2 [509, 23, 5] 6 C6
132) [509, 69, 45] [1] 2 [509, 69, 45] 6 C6
133) [113, 94, 401] [1] 1 [113, 94, 401] 3 C3
134) [113, 35, 52] [1] 1 [113, 35, 52] 3 C3
135) [113, 35, 52] [2] 1 [113, 35, 52] 3 C3
136) [113, 119, 1252] [1] 1 [113, 119, 1252] 3 C3
137) [857, 59, 656] [1] 1 [857, 59, 656] 3 C3
138) [89, 39, 180] [1] 2 [89, 39, 180] 6 C6
139) [89, 78, 97] [1] 1 [89, 78, 97] 3 C3
140) [1721, 43, 32] [1] 1 [1721, 43, 32] 3 C3
141) [53, 25, 37] [1] 1 [53, 25, 37] 3 C3
142) [53, 33, 153] [1] 2 [53, 33, 153] 6 C6
143) [53, 23, 13] [1] 2 [53, 23, 13] 6 C6
144) [937, 35, 72] [1] 1 [937, 35, 72] 3 C3
145) [1933, 49, 117] [1] 1 [1933, 49, 117] 3 C3
146) [281, 19, 20] [1] 1 [281, 19, 20] 3 C3
147) [37, 77, 733] [1] 1 [37, 77, 733] 3 C3
148) [37, 41, 337] [1] 1 [37, 41, 337] 3 C3
149) [37, 137, 613] [1] 1 [37, 137, 613] 3 C3
150) [37, 33, 41] [1] 1 [37, 33, 41] 3 C3
151) [37, 45, 53] [1] 1 [37, 45, 53] 3 C3
152) [37, 202, 10053] [1] 1 [37, 202, 10053] 3 C3
153) [37, 21, 101] [1] 1 [37, 21, 101] 3 C3
154) [2549, 77, 845] [1] 1 [2549, 77, 845] 3 C3
155) [617, 25, 2] [1] 1 [617, 25, 2] 3 C3
156) [61, 70, 981] [1] 2 [61, 70, 981] 6 C6
157) [61, 18, 20] [1] 2 [61, 18, 20] 6 C6
158) [61, 46, 468] [1] 2 [61, 46, 468] 6 C6
159) [61, 253, 14157] [1] 2 [61, 253, 14157] 6 C6
160) [61, 29, 73] [1] 1 [61, 29, 73] 3 C3
161) [197, 213, 261] [1] 2 [197, 213, 261] 6 C6
162) [1249, 39, 68] [1] 1 [1249, 39, 68] 3 C3
163) [593, 123, 2448] [1] 2 [593, 123, 2448] 6 C6
164) [593, 75, 72] [1] 2 [593, 75, 72] 6 C6
165) [17, 246, 5337] [1] 2 [17, 246, 5337] 6 C6
166) [17, 75, 1300] [1] 2 [17, 75, 1300] 6 C6
167) [17, 78, 1249] [1] 1 [17, 78, 1249] 3 C3
168) [17, 26, 101] [1] 1 [17, 26, 101] 3 C3
169) [17, 86, 761] [1] 1 [17, 86, 761] 3 C3
170) [17, 175, 7652] [1] 1 [17, 175, 7652] 3 C3
171) [17, 66, 477] [1] 2 [17, 66, 477] 6 C6
172) [17, 174, 5121] [1] 2 [17, 174, 5121] 6 C6
173) [17, 75, 1300] [2] 2 [17, 75, 1300] 6 C6
174) [17, 111, 3076] [1] 1 [17, 111, 3076] 3 C3
175) [17, 167, 6628] [1] 1 [17, 167, 6628] 3 C3
176) [17, 103, 2308] [1] 1 [17, 103, 2308] 3 C3
177) [373, 145, 2925] [1] 2 [373, 145, 2925] 6 C6
178) [173, 17, 29] [1] 1 [173, 17, 29] 3 C3
179) [2969, 59, 128] [1] 1 [2969, 59, 128] 3 C3
180) [1429, 77, 1125] [1] 1 [1429, 77, 1125] 15 C15
181) [1676, 82, 5] [1] 2 [1676, 82, 5] 6 C6
182) [2789, 53, 5] [1] 1 [2789, 53, 5] 3 C3
183) [181, 133, 2205] [1] 2 [181, 133, 2205] 6 C6
184) [761, 43, 272] [1] 1 [761, 43, 272] 9 C3 x C3
185) [1061, 177, 5445] [1] 2 [1061, 177, 5445] 6 C6
186) [524, 46, 5] [1] 2 [524, 46, 5] 6 C6
187) [2393, 49, 2] [1] 1 [2393, 49, 2] 3 C3
188) [569, 87, 612] [1] 2 [569, 87, 612] 6 C6
189) [569, 43, 320] [1] 1 [569, 43, 320] 3 C3
190) [701, 130, 1421] [1] 1 [701, 130, 1421] 3 C3
191) [701, 41, 245] [1] 1 [701, 41, 245] 3 C3
192) [1913, 139, 4352] [1] 1 [1913, 139, 4352] 3 C3
193) [1481, 41, 50] [1] 1 [1481, 41, 50] 3 C3
194) [44, 18, 37] [1] 2 [44, 18, 37] 6 C6
195) [44, 32, 212] [1] 2 [44, 32, 212] 6 C6
196) [44, 74, 269] [1] 2 [44, 74, 269] 6 C6
197) [44, 80, 1556] [1] 2 [44, 80, 1556] 6 C6
198) [44, 30, 181] [1] 2 [44, 30, 181] 6 C6
199) [337, 82, 333] [1] 1 [337, 82, 333] 3 C3
200) [337, 79, 1476] [1] 1 [337, 79, 1476] 3 C3
201) [389, 21, 13] [1] 1 [389, 21, 13] 3 C3
202) [613, 113, 1813] [1] 1 [613, 113, 1813] 3 C3
203) [12, 62, 373] [1] 2 [12, 62, 373] 6 C6
204) [12, 34, 181] [1] 2 [12, 34, 181] 6 C6
205) [12, 22, 109] [1] 2 [12, 22, 109] 6 C6
206) [12, 86, 877] [1] 2 [12, 86, 877] 6 C6
207) [12, 38, 349] [1] 2 [12, 38, 349] 6 C6
208) [12, 16, 37] [2] 4 [12, 16, 37] 6 C6
209) [12, 50, 613] [1] 2 [12, 50, 613] 6 C6
210) [12, 10, 13] [3, 3] 1 [12, 10, 13] 2 C2
211) [12, 16, 37] [1] 2 [12, 16, 37] 6 C6
212) [12, 74, 397] [1] 2 [12, 74, 397] 6 C6
213) [12, 62, 853] [1] 2 [12, 62, 853] 6 C6
214) [12, 62, 661] [1] 2 [12, 62, 661] 6 C6
215) [12, 32, 109] [1] 2 [12, 32, 109] 6 C6
216) [12, 56, 277] [1] 2 [12, 56, 277] 6 C6
217) [12, 32, 229] [1] 2 [12, 32, 229] 6 C6
218) [12, 70, 637] [1] 4 [12, 70, 637] 12 C2 x C6
219) [769, 87, 1700] [1] 1 [769, 87, 1700] 3 C3
220) [601, 27, 32] [1] 1 [601, 27, 32] 3 C3
221) [277, 67, 1053] [1] 2 [277, 67, 1053] 6 C6
222) [1004, 64, 20] [1] 2 [1004, 64, 20] 6 C6
223) [673, 83, 208] [1] 1 [673, 83, 208] 3 C3
224) [1181, 41, 125] [1] 1 [1181, 41, 125] 3 C3
225) [73, 58, 549] [1] 1 [73, 58, 549] 3 C3
226) [73, 78, 353] [1] 1 [73, 78, 353] 3 C3
227) [1193, 35, 8] [1] 1 [1193, 35, 8] 3 C3
228) [2309, 53, 125] [1] 1 [2309, 53, 125] 3 C3
229) [1097, 35, 32] [1] 1 [1097, 35, 32] 3 C3
230) [41, 21, 18] [1] 2 [41, 21, 18] 6 C6
231) [41, 111, 1348] [1] 1 [41, 111, 1348] 3 C3
232) [41, 151, 5444] [1] 1 [41, 151, 5444] 3 C3
233) [41, 31, 148] [2] 1 [41, 31, 148] 3 C3
234) [41, 118, 857] [1] 1 [41, 118, 857] 3 C3
235) [41, 31, 148] [1] 1 [41, 31, 148] 3 C3
236) [41, 103, 1412] [1] 1 [41, 103, 1412] 3 C3
237) [241, 199, 6948] [1] 1 [241, 199, 6948] 3 C3
238) [241, 31, 180] [1] 1 [241, 31, 180] 3 C3
239) [829, 57, 605] [1] 1 [829, 57, 605] 3 C3
240) [353, 57, 18] [1] 2 [353, 57, 18] 6 C6
241) [353, 39, 292] [1] 1 [353, 39, 292] 3 C3
242) [353, 107, 656] [1] 1 [353, 107, 656] 3 C3
243) [929, 47, 320] [1] 1 [929, 47, 320] 3 C3
244) [101, 13, 17] [1] 1 [101, 13, 17] 3 C3
245) [101, 22, 20] [1] 2 [101, 22, 20] 6 C6
246) [101, 42, 37] [1] 1 [101, 42, 37] 3 C3
247) [101, 77, 245] [1] 2 [101, 77, 245] 6 C6
248) [101, 11, 5] [1] 2 [101, 11, 5] 6 C6
249) [1949, 73, 845] [1] 1 [1949, 73, 845] 3 C3
250) [577, 55, 612] [1] 1 [577, 55, 612] 21 C21