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 200 Igusa CM invariants of non-normal (D4) fields: 161

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 377, 17701] [1] 1 [317, 377, 17701] 100 C100
2) [165, 937, 23101] [1] 1 [165, 937, 23101] 200 C2 x C100
3) [344, 264, 8824] [1] 1 [344, 264, 8824] 100 C2 x C50
4) [809, 1455, 495076] [1] 1 [809, 1455, 495076] 100 C100
5) [437, 885, 12157] [1] 1 [437, 885, 12157] 100 C100
6) [60, 766, 40849] [1] 1 [60, 766, 40849] 200 C2 x C2 x C50
7) [60, 994, 97009] [1] 1 [60, 994, 97009] 200 C2 x C10 x C10
8) [60, 218, 11641] [1] 1 [60, 218, 11641] 200 C2 x C100
9) [60, 562, 38401] [1] 1 [60, 562, 38401] 200 C2 x C2 x C50
10) [60, 334, 24049] [1] 1 [60, 334, 24049] 200 C2 x C100
11) [2729, 575, 76516] [1] 1 [2729, 575, 76516] 100 C2 x C50
12) [385, 211, 10264] [1] 1 [385, 211, 10264] 200 C2 x C100
13) [236, 90, 1966] [1] 1 [236, 90, 1966] 100 C2 x C50
14) [137, 771, 72952] [1] 1 [137, 771, 72952] 100 C2 x C50
15) [137, 1695, 705892] [1] 1 [137, 1695, 705892] 100 C10 x C10
16) [137, 798, 104401] [1] 1 [137, 798, 104401] 100 C100
17) [129, 910, 204961] [1] 1 [129, 910, 204961] 100 C2 x C50
18) [129, 1735, 743236] [1] 1 [129, 1735, 743236] 100 C2 x C50
19) [129, 277, 9862] [1] 1 [129, 277, 9862] 100 C2 x C50
20) [104, 202, 10097] [1] 1 [104, 202, 10097] 200 C2 x C2 x C50
21) [161, 365, 30046] [1] 1 [161, 365, 30046] 100 C2 x C50
22) [161, 1383, 439492] [1] 1 [161, 1383, 439492] 100 C100
23) [249, 1135, 236836] [1] 1 [249, 1135, 236836] 100 C100
24) [109, 201, 10073] [1] 1 [109, 201, 10073] 100 C100
25) [641, 1511, 534724] [1] 1 [641, 1511, 534724] 100 C100
26) [57, 1003, 75928] [1] 1 [57, 1003, 75928] 100 C2 x C50
27) [57, 811, 132952] [1] 1 [57, 811, 132952] 100 C2 x C50
28) [57, 193, 1774] [1] 1 [57, 193, 1774] 100 C2 x C50
29) [57, 715, 93592] [1] 1 [57, 715, 93592] 100 C2 x C50
30) [57, 277, 14038] [1] 1 [57, 277, 14038] 100 C10 x C10
31) [205, 153, 5801] [1] 1 [205, 153, 5801] 200 C10 x C20
32) [209, 915, 112696] [1] 1 [209, 915, 112696] 100 C2 x C50
33) [209, 1575, 592516] [1] 1 [209, 1575, 592516] 100 C2 x C50
34) [76, 102, 2297] [2, 2] 1 [76, 102, 2297] 50 C50
35) [8, 1718, 727513] [1] 1 [8, 1718, 727513] 100 C2 x C50
36) [8, 1842, 848041] [1] 1 [8, 1842, 848041] 100 C100
37) [8, 1458, 530473] [1] 1 [8, 1458, 530473] 100 C100
38) [8, 1558, 571993] [1] 1 [8, 1558, 571993] 100 C100
39) [8, 1222, 290089] [1] 1 [8, 1222, 290089] 100 C100
40) [5, 1277, 340981] [1] 1 [5, 1277, 340981] 100 C100
41) [5, 1686, 694969] [1] 1 [5, 1686, 694969] 100 C100
42) [5, 1286, 401929] [1] 1 [5, 1286, 401929] 100 C2 x C50
43) [5, 1597, 608341] [1] 1 [5, 1597, 608341] 100 C100
44) [5, 1654, 665929] [1] 1 [5, 1654, 665929] 100 C100
45) [5, 1717, 732061] [1] 1 [5, 1717, 732061] 100 C2 x C50
46) [5, 1686, 708649] [1] 1 [5, 1686, 708649] 100 C100
47) [5, 1517, 552541] [1] 1 [5, 1517, 552541] 100 C100
48) [29, 1037, 71461] [1] 1 [29, 1037, 71461] 100 C2 x C50
49) [92, 1138, 161473] [1] 1 [92, 1138, 161473] 100 C100
50) [124, 162, 4577] [1] 1 [124, 162, 4577] 100 C2 x C50
51) [3605, 141, 4069] [1] 1 [3605, 141, 4069] 200 C2 x C100
52) [24, 1510, 569161] [1] 1 [24, 1510, 569161] 100 C100
53) [24, 190, 8161] [2, 2] 1 [24, 190, 8161] 50 C50
54) [24, 430, 45841] [1] 1 [24, 430, 45841] 100 C5 x C20
55) [24, 1114, 232273] [1] 1 [24, 1114, 232273] 100 C10 x C10
56) [24, 1270, 298681] [1] 1 [24, 1270, 298681] 100 C100
57) [24, 1174, 198553] [1] 1 [24, 1174, 198553] 100 C5 x C20
58) [24, 1126, 278569] [1] 1 [24, 1126, 278569] 100 C2 x C50
59) [24, 286, 18913] [1] 1 [24, 286, 18913] 100 C100
60) [24, 1306, 325009] [1] 1 [24, 1306, 325009] 100 C100
61) [24, 1114, 167953] [1] 1 [24, 1114, 167953] 100 C100
62) [24, 874, 95713] [1] 1 [24, 874, 95713] 100 C100
63) [2905, 487, 52756] [1] 1 [2905, 487, 52756] 200 C2 x C100
64) [105, 1279, 376804] [1] 1 [105, 1279, 376804] 200 C2 x C100
65) [105, 1006, 170689] [1] 1 [105, 1006, 170689] 200 C2 x C2 x C50
66) [105, 691, 56344] [1] 1 [105, 691, 56344] 200 C2 x C100
67) [764, 398, 12097] [1] 1 [764, 398, 12097] 100 C100
68) [141, 202, 9637] [1] 1 [141, 202, 9637] 100 C2 x C50
69) [141, 173, 6601] [1] 1 [141, 173, 6601] 100 C2 x C50
70) [152, 174, 5137] [1] 1 [152, 174, 5137] 100 C100
71) [152, 1018, 93553] [1] 1 [152, 1018, 93553] 100 C100
72) [40, 256, 7384] [1] 1 [40, 256, 7384] 200 C2 x C100
73) [140, 774, 93769] [1] 1 [140, 774, 93769] 200 C2 x C100
74) [140, 942, 19681] [1] 1 [140, 942, 19681] 200 C2 x C100
75) [140, 806, 142249] [1] 1 [140, 806, 142249] 200 C2 x C2 x C50
76) [113, 242, 10573] [1] 1 [113, 242, 10573] 100 C100
77) [113, 317, 18766] [1] 1 [113, 317, 18766] 100 C2 x C50
78) [248, 998, 25801] [1] 1 [248, 998, 25801] 100 C100
79) [185, 249, 2134] [1] 1 [185, 249, 2134] 200 C2 x C100
80) [185, 747, 37336] [1] 1 [185, 747, 37336] 200 C2 x C100
81) [185, 1111, 308164] [1] 1 [185, 1111, 308164] 200 C200
82) [89, 819, 153784] [1] 1 [89, 819, 153784] 100 C2 x C50
83) [89, 831, 172084] [1] 1 [89, 831, 172084] 100 C100
84) [89, 1566, 577489] [1] 1 [89, 1566, 577489] 100 C10 x C10
85) [53, 993, 222013] [1] 1 [53, 993, 222013] 100 C100
86) [329, 1086, 163249] [1] 1 [329, 1086, 163249] 100 C100
87) [329, 451, 32344] [1] 1 [329, 451, 32344] 100 C2 x C50
88) [329, 855, 30676] [1] 1 [329, 855, 30676] 100 C100
89) [3160, 346, 1489] [1] 1 [3160, 346, 1489] 200 C2 x C100
90) [281, 619, 19288] [1] 1 [281, 619, 19288] 100 C100
91) [184, 162, 6377] [1] 1 [184, 162, 6377] 100 C2 x C50
92) [177, 526, 66337] [1] 1 [177, 526, 66337] 100 C100
93) [28, 778, 135193] [1] 1 [28, 778, 135193] 100 C5 x C20
94) [1677, 1045, 222277] [1] 1 [1677, 1045, 222277] 400 C2 x C200
95) [33, 325, 24022] [1] 1 [33, 325, 24022] 100 C2 x C50
96) [33, 991, 128692] [1] 1 [33, 991, 128692] 100 C100
97) [33, 1078, 237721] [1] 1 [33, 1078, 237721] 100 C2 x C50
98) [33, 1519, 571684] [1] 1 [33, 1519, 571684] 100 C10 x C10
99) [33, 1222, 297289] [1] 1 [33, 1222, 297289] 100 C100
100) [33, 861, 184662] [1] 1 [33, 861, 184662] 100 C10 x C10
101) [33, 1366, 432697] [1] 1 [33, 1366, 432697] 100 C2 x C50
102) [33, 925, 25798] [1] 1 [33, 925, 25798] 100 C2 x C50
103) [492, 898, 4801] [1] 1 [492, 898, 4801] 200 C2 x C100
104) [2924, 450, 3841] [1] 1 [2924, 450, 3841] 400 C2 x C200
105) [1461, 1189, 335533] [1] 1 [1461, 1189, 335533] 100 C2 x C50
106) [17, 297, 20518] [1] 1 [17, 297, 20518] 100 C100
107) [17, 1231, 361972] [1] 1 [17, 1231, 361972] 100 C5 x C20
108) [17, 1622, 647929] [1] 1 [17, 1622, 647929] 100 C100
109) [17, 1571, 613912] [1] 1 [17, 1571, 613912] 100 C2 x C50
110) [17, 1387, 444184] [1] 1 [17, 1387, 444184] 100 C2 x C50
111) [17, 249, 10294] [1] 1 [17, 249, 10294] 100 C100
112) [17, 1603, 622168] [1] 1 [17, 1603, 622168] 100 C10 x C10
113) [17, 1243, 377656] [1] 1 [17, 1243, 377656] 100 C100
114) [264, 706, 65209] [1] 1 [264, 706, 65209] 200 C10 x C20
115) [2801, 519, 33028] [1] 1 [2801, 519, 33028] 100 C100
116) [3473, 203, 2488] [1] 1 [3473, 203, 2488] 100 C5 x C20
117) [133, 189, 8897] [1] 1 [133, 189, 8897] 100 C2 x C50
118) [668, 558, 11041] [1] 1 [668, 558, 11041] 100 C5 x C20
119) [77, 822, 19849] [1] 1 [77, 822, 19849] 100 C5 x C20
120) [393, 175, 6772] [1] 1 [393, 175, 6772] 100 C100
121) [701, 981, 25909] [1] 1 [701, 981, 25909] 100 C100
122) [188, 154, 5177] [1] 1 [188, 154, 5177] 100 C2 x C50
123) [188, 898, 32401] [1] 1 [188, 898, 32401] 100 C100
124) [1145, 1007, 44836] [1] 1 [1145, 1007, 44836] 400 C2 x C200
125) [44, 1150, 329041] [1] 1 [44, 1150, 329041] 100 C100
126) [44, 1194, 246409] [1] 1 [44, 1194, 246409] 100 C2 x C50
127) [44, 1410, 485761] [1] 1 [44, 1410, 485761] 100 C2 x C50
128) [12, 1198, 341473] [1] 1 [12, 1198, 341473] 100 C2 x C50
129) [12, 922, 160249] [1] 1 [12, 922, 160249] 100 C10 x C10
130) [12, 334, 24817] [1] 1 [12, 334, 24817] 100 C2 x C50
131) [12, 1522, 541489] [1] 1 [12, 1522, 541489] 100 C10 x C10
132) [12, 1330, 380017] [1] 1 [12, 1330, 380017] 100 C2 x C50
133) [12, 1258, 298441] [1] 1 [12, 1258, 298441] 100 C2 x C50
134) [12, 1186, 328417] [1] 1 [12, 1186, 328417] 100 C2 x C50
135) [12, 1402, 432601] [1] 1 [12, 1402, 432601] 100 C10 x C10
136) [12, 382, 35713] [1] 1 [12, 382, 35713] 100 C2 x C50
137) [12, 1426, 505297] [1] 1 [12, 1426, 505297] 100 C2 x C50
138) [1545, 757, 96526] [1] 1 [1545, 757, 96526] 200 C2 x C100
139) [21, 1054, 84193] [1] 1 [21, 1054, 84193] 100 C2 x C50
140) [21, 1369, 386509] [1] 1 [21, 1369, 386509] 100 C2 x C50
141) [21, 886, 187849] [1] 1 [21, 886, 187849] 100 C2 x C50
142) [21, 1345, 408781] [1] 1 [21, 1345, 408781] 100 C2 x C50
143) [2417, 651, 3832] [1] 1 [2417, 651, 3832] 100 C100
144) [56, 296, 17368] [1] 1 [56, 296, 17368] 100 C2 x C50
145) [56, 302, 14737] [1] 1 [56, 302, 14737] 100 C100
146) [485, 645, 28225] [1] 1 [485, 645, 28225] 200 C200
147) [41, 899, 161368] [1] 1 [41, 899, 161368] 100 C2 x C50
148) [41, 827, 57976] [1] 1 [41, 827, 57976] 100 C100
149) [41, 461, 53038] [1] 1 [41, 461, 53038] 100 C2 x C50
150) [41, 939, 219928] [1] 1 [41, 939, 219928] 100 C2 x C50
151) [41, 1447, 465796] [1] 1 [41, 1447, 465796] 100 C2 x C50
152) [41, 241, 3358] [1] 1 [41, 241, 3358] 100 C2 x C50
153) [397, 157, 5269] [1] 1 [397, 157, 5269] 100 C100
154) [633, 157, 2206] [1] 1 [633, 157, 2206] 100 C2 x C50
155) [101, 669, 96109] [1] 1 [101, 669, 96109] 100 C100
156) [2345, 687, 18916] [1] 1 [2345, 687, 18916] 200 C2 x C100
157) [69, 1021, 70429] [1] 1 [69, 1021, 70429] 100 C100
158) [65, 1406, 484849] [1] 1 [65, 1406, 484849] 200 C2 x C2 x C50
159) [65, 1911, 912964] [1] 1 [65, 1911, 912964] 200 C2 x C100
160) [65, 1299, 401944] [1] 1 [65, 1299, 401944] 200 C2 x C100
161) [65, 1171, 202264] [1] 1 [65, 1171, 202264] 200 C2 x C100