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 240 Igusa CM invariants of non-normal (D4) fields: 164

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [661, 1182, 306977] [1] 1 [661, 1182, 306977] 120 C120
2) [165, 369, 29049] [1] 1 [165, 369, 29049] 240 C2 x C2 x C60
3) [165, 429, 45969] [1] 1 [165, 429, 45969] 240 C2 x C2 x C60
4) [437, 369, 20821] [1] 1 [437, 369, 20821] 120 C120
5) [437, 253, 7153] [1] 1 [437, 253, 7153] 120 C120
6) [60, 118, 1321] [2, 2] 1 [60, 118, 1321] 120 C2 x C2 x C30
7) [60, 342, 23241] [1] 1 [60, 342, 23241] 240 C4 x C60
8) [60, 474, 55929] [1] 1 [60, 474, 55929] 240 C4 x C60
9) [60, 282, 13881] [1] 1 [60, 282, 13881] 240 C4 x C60
10) [60, 374, 32809] [1] 1 [60, 374, 32809] 240 C4 x C60
11) [737, 279, 19276] [1] 1 [737, 279, 19276] 120 C2 x C60
12) [584, 338, 23305] [1] 1 [584, 338, 23305] 240 C4 x C60
13) [301, 321, 19665] [1] 2 [301, 321, 19665] 240 C2 x C2 x C2 x C30
14) [269, 377, 35465] [1] 1 [269, 377, 35465] 120 C2 x C60
15) [269, 453, 43165] [1] 1 [269, 453, 43165] 120 C2 x C60
16) [236, 266, 2585] [1] 1 [236, 266, 2585] 120 C2 x C60
17) [349, 361, 12949] [1] 1 [349, 361, 12949] 120 C120
18) [120, 886, 102169] [1] 1 [120, 886, 102169] 240 C2 x C2 x C2 x C30
19) [665, 606, 81169] [1] 1 [665, 606, 81169] 240 C4 x C60
20) [296, 562, 12361] [1] 1 [296, 562, 12361] 240 C2 x C2 x C60
21) [429, 293, 20497] [1] 1 [429, 293, 20497] 240 C2 x C2 x C60
22) [357, 273, 7833] [1] 1 [357, 273, 7833] 240 C2 x C2 x C60
23) [357, 309, 19497] [1] 1 [357, 309, 19497] 240 C4 x C60
24) [357, 293, 14233] [1] 1 [357, 293, 14233] 240 C2 x C2 x C60
25) [104, 298, 13777] [1] 1 [104, 298, 13777] 240 C2 x C2 x C60
26) [853, 1141, 120537] [1] 1 [853, 1141, 120537] 120 C120
27) [1544, 930, 29401] [1] 1 [1544, 930, 29401] 240 C2 x C120
28) [213, 321, 16761] [1] 1 [213, 321, 16761] 120 C2 x C60
29) [213, 238, 10753] [1] 1 [213, 238, 10753] 120 C120
30) [57, 326, 18361] [1] 1 [57, 326, 18361] 120 C2 x C60
31) [348, 266, 5161] [1] 1 [348, 266, 5161] 240 C2 x C2 x C60
32) [136, 358, 27145] [1] 1 [136, 358, 27145] 240 C4 x C60
33) [253, 361, 29481] [1] 1 [253, 361, 29481] 120 C2 x C60
34) [517, 253, 15873] [1] 1 [517, 253, 15873] 120 C2 x C2 x C30
35) [517, 241, 11289] [1] 1 [517, 241, 11289] 120 C2 x C60
36) [13, 449, 50137] [3, 3] 1 [13, 449, 50137] 30 C30
37) [13, 577, 82501] [1] 1 [13, 577, 82501] 120 C2 x C60
38) [13, 589, 86701] [1] 1 [13, 589, 86701] 120 C120
39) [13, 151, 5671] [1] 1 [13, 151, 5671] 120 C2 x C60
40) [220, 138, 3881] [1] 1 [220, 138, 3881] 240 C2 x C2 x C60
41) [8, 202, 9553] [3, 3] 1 [8, 202, 9553] 30 C30
42) [8, 110, 2225] [10, 10] 1 [8, 110, 2225] 12 C12
43) [280, 354, 28809] [1] 1 [280, 354, 28809] 240 C4 x C60
44) [5, 1238, 375161] [1] 1 [5, 1238, 375161] 120 C120
45) [5, 2006, 1005929] [1] 1 [5, 2006, 1005929] 120 C120
46) [5, 449, 50369] [5, 5] 1 [5, 449, 50369] 24 C2 x C12
47) [5, 1721, 733049] [1] 1 [5, 1721, 733049] 120 C120
48) [5, 1901, 898169] [1] 1 [5, 1901, 898169] 120 C120
49) [5, 1886, 888529] [1] 1 [5, 1886, 888529] 120 C120
50) [5, 2021, 1021049] [1] 1 [5, 2021, 1021049] 120 C120
51) [268, 346, 25641] [1] 1 [268, 346, 25641] 120 C2 x C60
52) [29, 1541, 578989] [1] 1 [29, 1541, 578989] 120 C120
53) [29, 29, 145] [5, 25] 1 [29, 29, 145] 6 C6
54) [941, 177, 7597] [1] 1 [941, 177, 7597] 120 C120
55) [124, 186, 8153] [1] 1 [124, 186, 8153] 120 C2 x C60
56) [124, 378, 31257] [1] 2 [124, 378, 31257] 240 C2 x C2 x C60
57) [440, 242, 3641] [1] 1 [440, 242, 3641] 240 C2 x C2 x C60
58) [93, 318, 23793] [1] 1 [93, 318, 23793] 120 C2 x C2 x C30
59) [93, 465, 54033] [1] 1 [93, 465, 54033] 120 C2 x C2 x C30
60) [93, 381, 32361] [1] 1 [93, 381, 32361] 120 C2 x C2 x C30
61) [589, 217, 11625] [5] 1 [589, 217, 11625] 24 C2 x C2 x C6
62) [24, 1510, 523561] [1] 1 [24, 1510, 523561] 120 C2 x C60
63) [413, 401, 31837] [1] 1 [413, 401, 31837] 120 C2 x C60
64) [285, 329, 21289] [1] 1 [285, 329, 21289] 240 C2 x C2 x C2 x C30
65) [285, 309, 15249] [1] 1 [285, 309, 15249] 240 C2 x C2 x C60
66) [428, 362, 17353] [1] 1 [428, 362, 17353] 120 C2 x C60
67) [408, 258, 6441] [1] 1 [408, 258, 6441] 240 C4 x C60
68) [40, 550, 74185] [1] 1 [40, 550, 74185] 240 C4 x C60
69) [140, 314, 15689] [1] 1 [140, 314, 15689] 240 C2 x C2 x C60
70) [509, 233, 7337] [1] 1 [509, 233, 7337] 120 C2 x C60
71) [113, 655, 105872] [1] 1 [113, 655, 105872] 120 C120
72) [521, 830, 97201] [1] 1 [521, 830, 97201] 120 C120
73) [168, 90, 513] [11] 1 [168, 90, 513] 24 C2 x C12
74) [168, 330, 18993] [1] 1 [168, 330, 18993] 240 C4 x C60
75) [89, 1355, 434776] [1] 1 [89, 1355, 434776] 120 C120
76) [565, 217, 8241] [1] 1 [565, 217, 8241] 240 C4 x C60
77) [497, 1383, 400516] [1] 1 [497, 1383, 400516] 120 C120
78) [497, 213, 5254] [1] 1 [497, 213, 5254] 120 C2 x C60
79) [1329, 967, 26116] [1] 1 [1329, 967, 26116] 120 C120
80) [53, 709, 73081] [1] 1 [53, 709, 73081] 120 C120
81) [53, 534, 70441] [1] 1 [53, 534, 70441] 120 C2 x C60
82) [341, 329, 24929] [1] 1 [341, 329, 24929] 120 C2 x C60
83) [2777, 543, 56356] [1] 1 [2777, 543, 56356] 360 C3 x C120
84) [712, 154, 5217] [1] 1 [712, 154, 5217] 240 C4 x C60
85) [37, 103, 1903] [1] 1 [37, 103, 1903] 120 C2 x C60
86) [37, 1337, 356233] [1] 1 [37, 1337, 356233] 120 C120
87) [37, 421, 34237] [1] 1 [37, 421, 34237] 120 C2 x C60
88) [536, 378, 35185] [1] 1 [536, 378, 35185] 120 C2 x C60
89) [536, 200, 5176] [1] 1 [536, 200, 5176] 120 C2 x C60
90) [293, 389, 21349] [1] 1 [293, 389, 21349] 120 C120
91) [28, 198, 9689] [2, 2] 1 [28, 198, 9689] 60 C60
92) [28, 562, 77953] [1] 1 [28, 562, 77953] 120 C2 x C60
93) [445, 285, 19305] [1] 1 [445, 285, 19305] 480 C2 x C2 x C120
94) [617, 335, 26668] [1] 1 [617, 335, 26668] 120 C2 x C60
95) [33, 318, 16833] [1] 1 [33, 318, 16833] 120 C2 x C60
96) [33, 418, 43549] [1] 1 [33, 418, 43549] 120 C2 x C2 x C30
97) [61, 126, 2993] [2, 2] 1 [61, 126, 2993] 40 C40
98) [61, 421, 42465] [1] 1 [61, 421, 42465] 120 C2 x C2 x C30
99) [61, 1177, 320697] [1] 1 [61, 1177, 320697] 120 C120
100) [593, 327, 19468] [1] 1 [593, 327, 19468] 120 C2 x C60
101) [3233, 327, 25924] [1] 1 [3233, 327, 25924] 240 C240
102) [881, 207, 10492] [1] 1 [881, 207, 10492] 120 C2 x C60
103) [17, 1731, 748984] [1] 1 [17, 1731, 748984] 120 C2 x C60
104) [17, 1902, 904129] [1] 1 [17, 1902, 904129] 120 C120
105) [17, 1931, 932152] [1] 1 [17, 1931, 932152] 120 C2 x C60
106) [17, 350, 26273] [1] 1 [17, 350, 26273] 120 C2 x C60
107) [1037, 1217, 208241] [1] 1 [1037, 1217, 208241] 240 C240
108) [264, 282, 6945] [1] 1 [264, 282, 6945] 240 C4 x C60
109) [264, 362, 30385] [1] 1 [264, 362, 30385] 240 C4 x C60
110) [173, 341, 21761] [1] 1 [173, 341, 21761] 120 C120
111) [173, 401, 38081] [1] 1 [173, 401, 38081] 120 C120
112) [545, 351, 24124] [1] 1 [545, 351, 24124] 240 C4 x C60
113) [2173, 817, 9873] [1] 1 [2173, 817, 9873] 240 C240
114) [645, 177, 3801] [1] 1 [645, 177, 3801] 240 C2 x C2 x C60
115) [773, 470, 5753] [1] 1 [773, 470, 5753] 120 C120
116) [573, 213, 7761] [1] 1 [573, 213, 7761] 120 C2 x C60
117) [232, 378, 33633] [1] 2 [232, 378, 33633] 480 C2 x C4 x C60
118) [232, 298, 10833] [1] 1 [232, 298, 10833] 240 C4 x C60
119) [232, 346, 24129] [1] 1 [232, 346, 24129] 240 C4 x C60
120) [133, 441, 48321] [1] 2 [133, 441, 48321] 240 C2 x C2 x C2 x C30
121) [776, 122, 2945] [1] 1 [776, 122, 2945] 240 C4 x C60
122) [668, 306, 20737] [1] 1 [668, 306, 20737] 120 C2 x C60
123) [77, 469, 54817] [1] 1 [77, 469, 54817] 120 C2 x C60
124) [77, 597, 88621] [1] 1 [77, 597, 88621] 120 C2 x C60
125) [701, 1613, 620825] [1] 1 [701, 1613, 620825] 120 C120
126) [701, 297, 21877] [1] 1 [701, 297, 21877] 120 C120
127) [188, 882, 103489] [1] 1 [188, 882, 103489] 120 C120
128) [653, 181, 6721] [1] 1 [653, 181, 6721] 120 C2 x C60
129) [44, 1386, 475849] [1] 1 [44, 1386, 475849] 120 C2 x C60
130) [44, 58, 137] [2, 14] 1 [44, 58, 137] 10 C10
131) [44, 1406, 454609] [1] 1 [44, 1406, 454609] 120 C120
132) [389, 193, 8437] [1] 1 [389, 193, 8437] 120 C2 x C60
133) [632, 314, 18961] [1] 1 [632, 314, 18961] 120 C120
134) [613, 205, 10353] [1] 1 [613, 205, 10353] 120 C2 x C2 x C30
135) [12, 142, 3313] [4, 4] 1 [12, 142, 3313] 30 C30
136) [12, 474, 55977] [1] 1 [12, 474, 55977] 120 C2 x C60
137) [12, 214, 11017] [2, 2] 1 [12, 214, 11017] 60 C2 x C30
138) [21, 245, 13825] [5, 5] 1 [21, 245, 13825] 24 C2 x C2 x C6
139) [21, 157, 5737] [3, 3] 1 [21, 157, 5737] 40 C40
140) [2417, 695, 71812] [1] 1 [2417, 695, 71812] 120 C120
141) [56, 178, 6521] [1] 1 [56, 178, 6521] 120 C120
142) [56, 382, 34465] [1] 1 [56, 382, 34465] 120 C2 x C60
143) [485, 401, 39109] [1] 1 [485, 401, 39109] 240 C4 x C60
144) [824, 234, 12865] [1] 1 [824, 234, 12865] 120 C2 x C60
145) [824, 98, 1577] [1] 1 [824, 98, 1577] 120 C120
146) [41, 579, 52804] [1] 1 [41, 579, 52804] 120 C120
147) [41, 1614, 650593] [1] 1 [41, 1614, 650593] 120 C120
148) [469, 277, 19065] [1] 1 [469, 277, 19065] 360 C2 x C6 x C30
149) [829, 1321, 306729] [1] 1 [829, 1321, 306729] 120 C120
150) [397, 313, 24393] [1] 1 [397, 313, 24393] 120 C2 x C60
151) [365, 289, 13489] [1] 1 [365, 289, 13489] 240 C4 x C60
152) [353, 471, 55372] [1] 1 [353, 471, 55372] 120 C2 x C60
153) [172, 706, 25537] [1] 1 [172, 706, 25537] 120 C120
154) [557, 345, 22933] [1] 1 [557, 345, 22933] 120 C2 x C60
155) [557, 233, 13433] [1] 1 [557, 233, 13433] 120 C2 x C60
156) [717, 153, 5673] [1] 1 [717, 153, 5673] 120 C2 x C60
157) [381, 317, 24265] [1] 1 [381, 317, 24265] 120 C2 x C60
158) [381, 297, 17385] [1] 1 [381, 297, 17385] 120 C2 x C2 x C30
159) [69, 217, 11617] [1] 1 [69, 217, 11617] 120 C120
160) [69, 805, 123901] [1] 1 [69, 805, 123901] 120 C2 x C60
161) [69, 366, 32385] [1] 1 [69, 366, 32385] 120 C2 x C2 x C30
162) [488, 386, 32857] [1] 1 [488, 386, 32857] 240 C4 x C60
163) [65, 1326, 388609] [1] 1 [65, 1326, 388609] 240 C4 x C60
164) [65, 591, 86524] [1] 1 [65, 591, 86524] 240 C4 x C60