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 320 Igusa CM invariants of non-normal (D4) fields: 215

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 1625, 618233] [1] 1 [317, 1625, 618233] 160 C4 x C40
2) [317, 1342, 404593] [1] 1 [317, 1342, 404593] 160 C160
3) [165, 1670, 433225] [1] 1 [165, 1670, 433225] 320 C4 x C80
4) [165, 1293, 408681] [1] 1 [165, 1293, 408681] 320 C4 x C80
5) [165, 1070, 72385] [1] 1 [165, 1070, 72385] 320 C4 x C80
6) [165, 1125, 182385] [1] 1 [165, 1125, 182385] 320 C2 x C4 x C40
7) [157, 742, 74841] [1] 1 [157, 742, 74841] 160 C2 x C2 x C40
8) [1672, 970, 32913] [1] 1 [1672, 970, 32913] 320 C4 x C80
9) [1228, 1042, 30753] [1] 1 [1228, 1042, 30753] 160 C2 x C80
10) [3436, 322, 12177] [1] 1 [3436, 322, 12177] 160 C2 x C80
11) [229, 829, 45345] [1] 1 [229, 829, 45345] 480 C2 x C240
12) [229, 1262, 218625] [1] 1 [229, 1262, 218625] 480 C2 x C2 x C120
13) [301, 669, 78705] [1] 1 [301, 669, 78705] 160 C2 x C2 x C40
14) [269, 809, 15065] [1] 1 [269, 809, 15065] 160 C2 x C80
15) [236, 778, 15385] [1] 1 [236, 778, 15385] 160 C2 x C80
16) [88, 1762, 765513] [1] 1 [88, 1762, 765513] 160 C2 x C80
17) [88, 1122, 275913] [1] 1 [88, 1122, 275913] 160 C2 x C80
18) [2181, 813, 7665] [1] 1 [2181, 813, 7665] 160 C2 x C2 x C40
19) [120, 1058, 36841] [1] 1 [120, 1058, 36841] 320 C4 x C80
20) [296, 698, 97825] [1] 1 [296, 698, 97825] 320 C4 x C80
21) [129, 955, 168376] [1] 1 [129, 955, 168376] 160 C2 x C2 x C40
22) [104, 1274, 368225] [1] 1 [104, 1274, 368225] 320 C4 x C80
23) [104, 1194, 343825] [1] 1 [104, 1194, 343825] 320 C4 x C80
24) [853, 334, 14241] [1] 1 [853, 334, 14241] 160 C4 x C40
25) [312, 642, 100233] [1] 1 [312, 642, 100233] 320 C4 x C80
26) [312, 834, 8841] [1] 1 [312, 834, 8841] 320 C4 x C80
27) [312, 982, 30169] [1] 1 [312, 982, 30169] 320 C2 x C2 x C80
28) [249, 277, 8662] [1] 1 [249, 277, 8662] 160 C2 x C2 x C40
29) [2328, 882, 192153] [1] 1 [2328, 882, 192153] 640 C8 x C80
30) [2328, 834, 115689] [1] 1 [2328, 834, 115689] 640 C8 x C80
31) [57, 782, 21553] [1] 1 [57, 782, 21553] 160 C160
32) [348, 474, 43641] [1] 1 [348, 474, 43641] 320 C4 x C80
33) [205, 841, 63609] [1] 1 [205, 841, 63609] 320 C2 x C4 x C40
34) [205, 1510, 517545] [1] 1 [205, 1510, 517545] 320 C2 x C4 x C40
35) [2681, 591, 70564] [1] 1 [2681, 591, 70564] 160 C2 x C80
36) [3229, 421, 24129] [1] 1 [3229, 421, 24129] 480 C480
37) [2269, 913, 207825] [1] 1 [2269, 913, 207825] 160 C2 x C80
38) [1752, 1044, 20196] [1] 1 [1752, 1044, 20196] 640 C8 x C80
39) [309, 653, 100345] [1] 1 [309, 653, 100345] 160 C2 x C2 x C40
40) [309, 1398, 468825] [1] 1 [309, 1398, 468825] 160 C2 x C2 x C40
41) [380, 1190, 279545] [1] 1 [380, 1190, 279545] 320 C4 x C80
42) [888, 1554, 581529] [1] 1 [888, 1554, 581529] 320 C4 x C80
43) [1384, 1258, 327825] [1] 1 [1384, 1258, 327825] 960 C2 x C2 x C240
44) [1837, 121, 3201] [1] 1 [1837, 121, 3201] 160 C2 x C80
45) [136, 1402, 452097] [1] 1 [136, 1402, 452097] 320 C4 x C80
46) [517, 942, 147393] [1] 1 [517, 942, 147393] 160 C4 x C40
47) [1265, 1047, 106756] [1] 1 [1265, 1047, 106756] 320 C2 x C160
48) [1381, 1213, 268065] [1] 1 [1381, 1213, 268065] 160 C2 x C2 x C40
49) [13, 1549, 542361] [1] 1 [13, 1549, 542361] 160 C2 x C80
50) [13, 1621, 613929] [1] 1 [13, 1621, 613929] 160 C2 x C80
51) [13, 1822, 824721] [1] 1 [13, 1822, 824721] 160 C2 x C2 x C40
52) [13, 1801, 797169] [1] 1 [13, 1801, 797169] 160 C2 x C80
53) [13, 1894, 891609] [1] 1 [13, 1894, 891609] 160 C4 x C40
54) [76, 1654, 647145] [1] 1 [76, 1654, 647145] 160 C2 x C80
55) [1997, 1009, 214081] [1] 1 [1997, 1009, 214081] 160 C160
56) [1285, 1141, 155529] [1] 1 [1285, 1141, 155529] 320 C8 x C40
57) [1741, 1153, 311025] [1] 1 [1741, 1153, 311025] 160 C2 x C2 x C40
58) [8, 1310, 335713] [1] 1 [8, 1310, 335713] 160 C2 x C80
59) [8, 1850, 855233] [1] 1 [8, 1850, 855233] 160 C160
60) [8, 1322, 434033] [1] 1 [8, 1322, 434033] 160 C2 x C80
61) [8, 1406, 457217] [1] 1 [8, 1406, 457217] 160 C2 x C80
62) [8, 1274, 259969] [1] 1 [8, 1274, 259969] 160 C2 x C80
63) [8, 986, 238817] [1] 1 [8, 986, 238817] 160 C160
64) [8, 1466, 534977] [1] 1 [8, 1466, 534977] 160 C160
65) [8, 1402, 403201] [1] 1 [8, 1402, 403201] 160 C160
66) [8, 1646, 655697] [1] 1 [8, 1646, 655697] 160 C2 x C80
67) [280, 1186, 250569] [1] 1 [280, 1186, 250569] 320 C4 x C80
68) [5, 2021, 1021009] [1] 1 [5, 2021, 1021009] 160 C4 x C40
69) [5, 1462, 499081] [1] 1 [5, 1462, 499081] 160 C2 x C80
70) [5, 1726, 733249] [1] 1 [5, 1726, 733249] 160 C2 x C80
71) [5, 2033, 1033241] [1] 1 [5, 2033, 1033241] 160 C2 x C2 x C40
72) [5, 1705, 699745] [1] 1 [5, 1705, 699745] 160 C2 x C80
73) [5, 1741, 756409] [1] 1 [5, 1741, 756409] 160 C2 x C80
74) [5, 1985, 984905] [1] 1 [5, 1985, 984905] 160 C4 x C40
75) [5, 1990, 989305] [1] 1 [5, 1990, 989305] 160 C4 x C40
76) [5, 1745, 739145] [1] 1 [5, 1745, 739145] 160 C2 x C2 x C40
77) [29, 1109, 294065] [1] 1 [29, 1109, 294065] 160 C4 x C40
78) [29, 1366, 362089] [1] 1 [29, 1366, 362089] 160 C2 x C2 x C40
79) [29, 1541, 541289] [1] 1 [29, 1541, 541289] 160 C2 x C80
80) [29, 1598, 615665] [1] 1 [29, 1598, 615665] 160 C2 x C80
81) [1804, 1018, 143625] [1] 1 [1804, 1018, 143625] 320 C4 x C80
82) [124, 1222, 229977] [1] 1 [124, 1222, 229977] 160 C2 x C80
83) [93, 1142, 205513] [1] 1 [93, 1142, 205513] 160 C2 x C2 x C40
84) [93, 1062, 101913] [1] 1 [93, 1062, 101913] 160 C2 x C2 x C40
85) [93, 1569, 590121] [1] 1 [93, 1569, 590121] 160 C2 x C2 x C40
86) [1416, 1178, 232225] [1] 1 [1416, 1178, 232225] 320 C4 x C80
87) [589, 798, 74385] [1] 1 [589, 798, 74385] 160 C2 x C2 x C40
88) [1720, 114, 1529] [1] 1 [1720, 114, 1529] 320 C2 x C2 x C80
89) [2701, 673, 80145] [1] 1 [2701, 673, 80145] 320 C4 x C80
90) [24, 1498, 524497] [1] 1 [24, 1498, 524497] 160 C160
91) [24, 1118, 270145] [1] 1 [24, 1118, 270145] 160 C2 x C80
92) [24, 1058, 262345] [1] 1 [24, 1058, 262345] 160 C2 x C80
93) [24, 1406, 407809] [1] 1 [24, 1406, 407809] 160 C2 x C80
94) [1205, 1025, 9305] [1] 1 [1205, 1025, 9305] 320 C2 x C2 x C80
95) [413, 917, 19313] [1] 1 [413, 917, 19313] 160 C2 x C80
96) [105, 1447, 511876] [1] 1 [105, 1447, 511876] 320 C2 x C160
97) [105, 1222, 265801] [1] 1 [105, 1222, 265801] 320 C2 x C160
98) [105, 1207, 239236] [1] 1 [105, 1207, 239236] 320 C2 x C160
99) [2524, 778, 141225] [1] 1 [2524, 778, 141225] 160 C2 x C80
100) [764, 1018, 11545] [1] 1 [764, 1018, 11545] 160 C160
101) [408, 1394, 394009] [1] 1 [408, 1394, 394009] 320 C4 x C80
102) [1093, 1477, 531993] [1] 1 [1093, 1477, 531993] 800 C2 x C10 x C40
103) [40, 1146, 310689] [1] 1 [40, 1146, 310689] 320 C4 x C80
104) [40, 1546, 596529] [1] 1 [40, 1546, 596529] 320 C4 x C80
105) [40, 1518, 540081] [1] 1 [40, 1518, 540081] 320 C4 x C80
106) [40, 1726, 725409] [1] 1 [40, 1726, 725409] 320 C4 x C80
107) [728, 470, 29017] [1] 1 [728, 470, 29017] 320 C2 x C2 x C80
108) [113, 1430, 446137] [1] 1 [113, 1430, 446137] 160 C160
109) [1229, 1289, 326585] [1] 1 [1229, 1289, 326585] 480 C4 x C120
110) [185, 381, 35134] [1] 1 [185, 381, 35134] 320 C4 x C80
111) [1660, 896, 119364] [1] 1 [1660, 896, 119364] 320 C4 x C80
112) [1144, 146, 4185] [1] 1 [1144, 146, 4185] 320 C4 x C80
113) [168, 714, 22449] [1] 1 [168, 714, 22449] 320 C4 x C80
114) [168, 154, 4417] [1] 1 [168, 154, 4417] 320 C2 x C2 x C80
115) [156, 1574, 568825] [1] 1 [156, 1574, 568825] 320 C4 x C80
116) [533, 1757, 765233] [1] 1 [533, 1757, 765233] 320 C4 x C80
117) [53, 1142, 241241] [1] 1 [53, 1142, 241241] 160 C2 x C2 x C40
118) [53, 1121, 138929] [1] 1 [53, 1121, 138929] 160 C2 x C80
119) [1941, 965, 123625] [1] 1 [1941, 965, 123625] 160 C2 x C80
120) [1437, 1269, 359121] [1] 1 [1437, 1269, 359121] 160 C4 x C40
121) [709, 1009, 11865] [1] 1 [709, 1009, 11865] 160 C2 x C2 x C40
122) [184, 1618, 623385] [1] 1 [184, 1618, 623385] 160 C2 x C80
123) [1373, 1349, 446369] [1] 1 [1373, 1349, 446369] 480 C2 x C240
124) [37, 1174, 173481] [1] 1 [37, 1174, 173481] 160 C2 x C2 x C40
125) [37, 1502, 563409] [1] 1 [37, 1502, 563409] 160 C2 x C2 x C40
126) [37, 1461, 463617] [1] 1 [37, 1461, 463617] 160 C2 x C2 x C40
127) [37, 1129, 307329] [1] 1 [37, 1129, 307329] 160 C2 x C2 x C40
128) [789, 1173, 154425] [1] 1 [789, 1173, 154425] 160 C2 x C80
129) [364, 1222, 301977] [1] 1 [364, 1222, 301977] 320 C4 x C80
130) [3036, 498, 13425] [1] 1 [3036, 498, 13425] 640 C2 x C4 x C80
131) [28, 770, 33537] [1] 1 [28, 770, 33537] 160 C2 x C80
132) [28, 1066, 270537] [1] 1 [28, 1066, 270537] 160 C2 x C80
133) [28, 848, 164964] [1] 1 [28, 848, 164964] 160 C2 x C80
134) [28, 1274, 324121] [1] 1 [28, 1274, 324121] 160 C2 x C80
135) [28, 1632, 295556] [1] 1 [28, 1632, 295556] 160 C160
136) [465, 886, 77209] [1] 1 [465, 886, 77209] 320 C2 x C2 x C2 x C40
137) [204, 1002, 133497] [1] 1 [204, 1002, 133497] 320 C4 x C80
138) [33, 1087, 281524] [1] 1 [33, 1087, 281524] 160 C160
139) [33, 1486, 526177] [1] 1 [33, 1486, 526177] 160 C2 x C80
140) [33, 1846, 849817] [1] 1 [33, 1846, 849817] 160 C4 x C40
141) [61, 1318, 316185] [1] 1 [61, 1318, 316185] 160 C2 x C2 x C40
142) [61, 1713, 716985] [1] 1 [61, 1713, 716985] 160 C2 x C2 x C40
143) [61, 1261, 378849] [1] 1 [61, 1261, 378849] 160 C4 x C40
144) [197, 454, 23161] [1] 1 [197, 454, 23161] 160 C2 x C80
145) [541, 1717, 720657] [1] 1 [541, 1717, 720657] 160 C2 x C80
146) [2392, 850, 178233] [1] 1 [2392, 850, 178233] 320 C4 x C80
147) [1661, 953, 7385] [1] 1 [1661, 953, 7385] 160 C2 x C2 x C40
148) [1661, 1193, 335465] [1] 1 [1661, 1193, 335465] 160 C4 x C40
149) [1608, 898, 7033] [1] 1 [1608, 898, 7033] 320 C2 x C160
150) [3544, 274, 15225] [1] 1 [3544, 274, 15225] 160 C2 x C80
151) [456, 1370, 366625] [1] 1 [456, 1370, 366625] 320 C4 x C80
152) [1505, 1079, 206404] [1] 1 [1505, 1079, 206404] 320 C4 x C80
153) [173, 985, 102037] [1] 1 [173, 985, 102037] 160 C2 x C80
154) [645, 686, 24769] [1] 1 [645, 686, 24769] 320 C4 x C80
155) [2204, 938, 211145] [1] 1 [2204, 938, 211145] 320 C4 x C80
156) [181, 598, 86505] [1] 1 [181, 598, 86505] 160 C2 x C2 x C40
157) [232, 138, 4529] [1] 1 [232, 138, 4529] 320 C2 x C2 x C80
158) [133, 966, 214137] [1] 1 [133, 966, 214137] 160 C2 x C2 x C40
159) [133, 1969, 968409] [1] 1 [133, 1969, 968409] 160 C2 x C2 x C40
160) [524, 838, 5785] [1] 1 [524, 838, 5785] 160 C2 x C80
161) [3116, 458, 2585] [1] 1 [3116, 458, 2585] 320 C4 x C80
162) [2076, 938, 145225] [1] 1 [2076, 938, 145225] 320 C4 x C80
163) [77, 809, 117401] [1] 1 [77, 809, 117401] 160 C2 x C2 x C40
164) [620, 1160, 8420] [1] 1 [620, 1160, 8420] 320 C4 x C80
165) [44, 898, 123985] [1] 1 [44, 898, 123985] 160 C2 x C80
166) [44, 1574, 613033] [1] 1 [44, 1574, 613033] 160 C160
167) [389, 1673, 664625] [1] 1 [389, 1673, 664625] 160 C2 x C80
168) [389, 982, 17017] [1] 1 [389, 982, 17017] 160 C2 x C2 x C40
169) [12, 1194, 263481] [1] 1 [12, 1194, 263481] 160 C2 x C80
170) [12, 1706, 712057] [1] 1 [12, 1706, 712057] 160 C2 x C80
171) [12, 1074, 282561] [1] 1 [12, 1074, 282561] 160 C2 x C80
172) [12, 1242, 235113] [1] 1 [12, 1242, 235113] 160 C2 x C80
173) [12, 1502, 520801] [1] 1 [12, 1502, 520801] 160 C2 x C80
174) [12, 1490, 520033] [1] 1 [12, 1490, 520033] 160 C2 x C80
175) [12, 1206, 218409] [1] 1 [12, 1206, 218409] 160 C2 x C80
176) [1932, 882, 1281] [1] 1 [1932, 882, 1281] 640 C4 x C4 x C40
177) [1545, 991, 106084] [1] 1 [1545, 991, 106084] 320 C2 x C2 x C80
178) [21, 1069, 264853] [1] 1 [21, 1069, 264853] 160 C2 x C80
179) [21, 1673, 695905] [1] 1 [21, 1673, 695905] 160 C2 x C2 x C40
180) [21, 1353, 450465] [1] 1 [21, 1353, 450465] 160 C2 x C2 x C40
181) [21, 1701, 701169] [1] 1 [21, 1701, 701169] 160 C2 x C2 x C40
182) [21, 1326, 405969] [1] 1 [21, 1326, 405969] 160 C2 x C2 x C40
183) [21, 1269, 266505] [1] 1 [21, 1269, 266505] 160 C2 x C2 x C40
184) [21, 1405, 480901] [1] 1 [21, 1405, 480901] 160 C2 x C80
185) [21, 1817, 823057] [1] 1 [21, 1817, 823057] 160 C2 x C80
186) [21, 1761, 768849] [1] 1 [21, 1761, 768849] 160 C2 x C2 x C40
187) [21, 1302, 326697] [1] 1 [21, 1302, 326697] 160 C2 x C2 x C40
188) [85, 901, 113169] [1] 1 [85, 901, 113169] 320 C2 x C4 x C40
189) [2620, 730, 122745] [1] 1 [2620, 730, 122745] 320 C4 x C80
190) [277, 1069, 169281] [1] 1 [277, 1069, 169281] 160 C160
191) [3189, 449, 43225] [1] 1 [3189, 449, 43225] 160 C4 x C40
192) [233, 895, 199732] [1] 1 [233, 895, 199732] 160 C2 x C80
193) [2317, 777, 20601] [1] 1 [2317, 777, 20601] 160 C2 x C2 x C40
194) [56, 360, 29656] [1] 1 [56, 360, 29656] 160 C2 x C80
195) [56, 562, 38137] [1] 1 [56, 562, 38137] 160 C160
196) [3237, 405, 1353] [1] 1 [3237, 405, 1353] 320 C4 x C80
197) [2360, 770, 32585] [1] 1 [2360, 770, 32585] 320 C4 x C80
198) [856, 162, 5705] [1] 1 [856, 162, 5705] 160 C2 x C80
199) [469, 1393, 386505] [1] 1 [469, 1393, 386505] 480 C2 x C2 x C120
200) [284, 1318, 342265] [1] 1 [284, 1318, 342265] 160 C2 x C80
201) [284, 1258, 303625] [1] 1 [284, 1258, 303625] 160 C2 x C80
202) [1885, 925, 43785] [1] 1 [1885, 925, 43785] 640 C4 x C4 x C40
203) [172, 1146, 229257] [1] 1 [172, 1146, 229257] 160 C2 x C80
204) [1324, 1186, 219249] [1] 1 [1324, 1186, 219249] 160 C2 x C80
205) [381, 1493, 487825] [1] 1 [381, 1493, 487825] 160 C2 x C80
206) [69, 1557, 550017] [1] 1 [69, 1557, 550017] 160 C4 x C40
207) [69, 838, 41977] [1] 1 [69, 838, 41977] 160 C2 x C80
208) [69, 1257, 245817] [1] 1 [69, 1257, 245817] 160 C2 x C2 x C40
209) [69, 1101, 230169] [1] 1 [69, 1101, 230169] 160 C2 x C80
210) [1045, 1105, 85545] [1] 1 [1045, 1105, 85545] 640 C2 x C8 x C40
211) [1084, 1474, 525825] [1] 1 [1084, 1474, 525825] 160 C2 x C80
212) [3853, 121, 2697] [1] 1 [3853, 121, 2697] 160 C4 x C40
213) [989, 1373, 382025] [1] 1 [989, 1373, 382025] 160 C2 x C80
214) [1309, 1213, 249705] [1] 1 [1309, 1213, 249705] 320 C4 x C80
215) [1309, 1333, 404625] [1] 1 [1309, 1333, 404625] 320 C2 x C4 x C40