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 140 Igusa CM invariants of non-normal (D4) fields: 222

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [1893, 77, 1009] [1] 1 [1893, 77, 1009] 70 C70
2) [2429, 729, 132253] [1] 1 [2429, 729, 132253] 210 C210
3) [661, 513, 6137] [1] 2 [661, 513, 6137] 140 C140
4) [737, 1031, 65092] [1] 1 [737, 1031, 65092] 70 C70
5) [584, 1634, 662233] [1] 1 [584, 1634, 662233] 140 C140
6) [229, 545, 32521] [1] 1 [229, 545, 32521] 210 C210
7) [629, 945, 7981] [1] 1 [629, 945, 7981] 140 C140
8) [88, 710, 57033] [1] 1 [88, 710, 57033] 70 C70
9) [296, 266, 7033] [1] 2 [296, 266, 7033] 280 C2 x C140
10) [104, 306, 16753] [1] 2 [104, 306, 16753] 280 C2 x C140
11) [104, 394, 8753] [1] 1 [104, 394, 8753] 140 C2 x C70
12) [104, 950, 90841] [1] 1 [104, 950, 90841] 140 C2 x C70
13) [461, 529, 8993] [1] 2 [461, 529, 8993] 140 C2 x C70
14) [161, 1751, 757444] [1] 1 [161, 1751, 757444] 70 C70
15) [109, 749, 128233] [1] 2 [109, 749, 128233] 140 C2 x C70
16) [109, 605, 71641] [1] 1 [109, 605, 71641] 70 C70
17) [1021, 429, 2873] [1] 2 [1021, 429, 2873] 140 C140
18) [57, 470, 10537] [1] 1 [57, 470, 10537] 70 C70
19) [57, 2038, 104473] [1] 1 [57, 2038, 104473] 70 C70
20) [205, 573, 80801] [1] 1 [205, 573, 80801] 140 C140
21) [309, 97, 1657] [1] 1 [309, 97, 1657] 70 C70
22) [3401, 239, 6628] [1] 1 [3401, 239, 6628] 70 C70
23) [377, 285, 17950] [1] 2 [377, 285, 17950] 280 C2 x C140
24) [517, 602, 88533] [1] 1 [517, 602, 88533] 70 C70
25) [209, 943, 165412] [1] 1 [209, 943, 165412] 70 C70
26) [209, 999, 161668] [1] 1 [209, 999, 161668] 70 C70
27) [13, 597, 46121] [1] 1 [13, 597, 46121] 70 C70
28) [13, 1005, 252425] [1] 2 [13, 1005, 252425] 140 C2 x C70
29) [13, 905, 201217] [1] 1 [13, 905, 201217] 70 C70
30) [13, 310, 16537] [1] 1 [13, 310, 16537] 70 C70
31) [13, 649, 46069] [1] 1 [13, 649, 46069] 70 C70
32) [13, 157, 3793] [3, 3] 1 [13, 157, 3793] 35 C35
33) [13, 821, 161929] [1] 1 [13, 821, 161929] 70 C70
34) [76, 398, 28657] [1] 1 [76, 398, 28657] 70 C70
35) [76, 186, 7433] [1] 1 [76, 186, 7433] 70 C70
36) [1285, 357, 16121] [1] 1 [1285, 357, 16121] 140 C140
37) [8, 1270, 346777] [1] 1 [8, 1270, 346777] 70 C70
38) [8, 430, 35857] [1] 1 [8, 430, 35857] 70 C70
39) [8, 526, 38417] [1] 1 [8, 526, 38417] 70 C70
40) [8, 1494, 538009] [1] 1 [8, 1494, 538009] 70 C70
41) [8, 1942, 647929] [1] 1 [8, 1942, 647929] 70 C70
42) [8, 1730, 744697] [1] 1 [8, 1730, 744697] 70 C70
43) [8, 184, 8014] [1] 1 [8, 184, 8014] 70 C70
44) [8, 810, 114097] [1] 1 [8, 810, 114097] 70 C70
45) [8, 1798, 807913] [1] 1 [8, 1798, 807913] 70 C70
46) [8, 810, 160497] [1] 2 [8, 810, 160497] 140 C2 x C70
47) [8, 1686, 710137] [1] 1 [8, 1686, 710137] 70 C70
48) [8, 1298, 248329] [1] 1 [8, 1298, 248329] 70 C70
49) [8, 1590, 606937] [1] 1 [8, 1590, 606937] 70 C70
50) [8, 778, 141521] [1] 1 [8, 778, 141521] 70 C70
51) [5, 1989, 805669] [1] 1 [5, 1989, 805669] 70 C70
52) [5, 1601, 613789] [1] 1 [5, 1601, 613789] 70 C70
53) [5, 934, 216089] [1] 1 [5, 934, 216089] 70 C70
54) [5, 1126, 291049] [1] 1 [5, 1126, 291049] 70 C70
55) [5, 577, 82321] [1] 1 [5, 577, 82321] 70 C70
56) [5, 1321, 402229] [1] 1 [5, 1321, 402229] 70 C70
57) [5, 893, 185581] [1] 1 [5, 893, 185581] 70 C70
58) [5, 1357, 446581] [1] 1 [5, 1357, 446581] 70 C70
59) [5, 1306, 347029] [1] 1 [5, 1306, 347029] 70 C70
60) [5, 989, 244249] [1] 1 [5, 989, 244249] 70 C70
61) [5, 1609, 640189] [1] 1 [5, 1609, 640189] 70 C70
62) [5, 757, 125561] [1] 1 [5, 757, 125561] 70 C70
63) [5, 742, 127961] [1] 1 [5, 742, 127961] 70 C70
64) [5, 1337, 412861] [1] 1 [5, 1337, 412861] 70 C70
65) [5, 1218, 301261] [1] 1 [5, 1218, 301261] 70 C70
66) [5, 966, 223609] [1] 1 [5, 966, 223609] 70 C70
67) [5, 1461, 532429] [1] 1 [5, 1461, 532429] 70 C70
68) [5, 1557, 580501] [1] 1 [5, 1557, 580501] 70 C70
69) [5, 1173, 340981] [1] 1 [5, 1173, 340981] 70 C70
70) [5, 901, 193489] [1] 1 [5, 901, 193489] 70 C70
71) [5, 1861, 864469] [1] 1 [5, 1861, 864469] 70 C70
72) [5, 1409, 407209] [1] 1 [5, 1409, 407209] 70 C70
73) [5, 133, 4361] [7, 7] 1 [5, 133, 4361] 10 C10
74) [5, 917, 208321] [1] 1 [5, 917, 208321] 70 C70
75) [5, 1037, 264781] [1] 1 [5, 1037, 264781] 70 C70
76) [5, 926, 196369] [1] 1 [5, 926, 196369] 70 C70
77) [5, 1134, 313489] [1] 1 [5, 1134, 313489] 70 C70
78) [5, 1829, 836029] [1] 1 [5, 1829, 836029] 70 C70
79) [268, 818, 157633] [1] 1 [268, 818, 157633] 70 C70
80) [29, 637, 92561] [1] 2 [29, 637, 92561] 140 C2 x C70
81) [29, 246, 13273] [1] 1 [29, 246, 13273] 70 C70
82) [29, 678, 98217] [1] 2 [29, 678, 98217] 140 C2 x C70
83) [29, 517, 14441] [1] 1 [29, 517, 14441] 70 C70
84) [29, 529, 62993] [1] 1 [29, 529, 62993] 70 C70
85) [92, 1018, 47113] [1] 1 [92, 1018, 47113] 70 C70
86) [124, 410, 17721] [1] 1 [124, 410, 17721] 70 C70
87) [93, 521, 32497] [1] 1 [93, 521, 32497] 70 C70
88) [93, 373, 2953] [1] 1 [93, 373, 2953] 70 C70
89) [93, 262, 3769] [1] 1 [93, 262, 3769] 70 C70
90) [93, 462, 39969] [1] 1 [93, 462, 39969] 70 C70
91) [24, 590, 86161] [1] 1 [24, 590, 86161] 70 C70
92) [24, 346, 28393] [1] 2 [24, 346, 28393] 140 C2 x C70
93) [24, 434, 40153] [1] 1 [24, 434, 40153] 70 C70
94) [24, 1036, 181924] [1] 2 [24, 1036, 181924] 140 C2 x C70
95) [221, 174, 4033] [1] 1 [221, 174, 4033] 140 C140
96) [221, 729, 10813] [1] 1 [221, 729, 10813] 140 C140
97) [221, 145, 5201] [1] 1 [221, 145, 5201] 140 C140
98) [221, 601, 85825] [1] 1 [221, 601, 85825] 140 C140
99) [781, 573, 58457] [1] 1 [781, 573, 58457] 70 C70
100) [141, 409, 3433] [1] 1 [141, 409, 3433] 70 C70
101) [40, 282, 5441] [1] 1 [40, 282, 5441] 140 C2 x C70
102) [40, 542, 21601] [1] 1 [40, 542, 21601] 140 C2 x C70
103) [40, 506, 55009] [1] 1 [40, 506, 55009] 140 C2 x C70
104) [149, 181, 8153] [1] 1 [149, 181, 8153] 70 C70
105) [149, 341, 20689] [1] 1 [149, 341, 20689] 70 C70
106) [140, 414, 42709] [1] 2 [140, 414, 42709] 280 C2 x C140
107) [248, 938, 110593] [1] 2 [248, 938, 110593] 140 C2 x C70
108) [248, 762, 13969] [1] 1 [248, 762, 13969] 70 C70
109) [156, 1000, 80116] [1] 2 [156, 1000, 80116] 280 C2 x C140
110) [156, 310, 16381] [1] 2 [156, 310, 16381] 280 C2 x C140
111) [89, 290, 17821] [1] 1 [89, 290, 17821] 70 C70
112) [89, 1398, 124057] [1] 1 [89, 1398, 124057] 70 C70
113) [305, 1031, 149764] [1] 1 [305, 1031, 149764] 140 C140
114) [533, 1617, 637549] [1] 1 [533, 1617, 637549] 140 C140
115) [53, 582, 77049] [1] 2 [53, 582, 77049] 140 C2 x C70
116) [53, 630, 68697] [1] 2 [53, 630, 68697] 140 C2 x C70
117) [53, 321, 14617] [1] 1 [53, 321, 14617] 70 C70
118) [53, 641, 96877] [1] 1 [53, 641, 96877] 70 C70
119) [53, 633, 90513] [1] 2 [53, 633, 90513] 140 C2 x C70
120) [53, 985, 242225] [1] 2 [53, 985, 242225] 140 C140
121) [1933, 57, 329] [1] 1 [1933, 57, 329] 70 C70
122) [1437, 281, 2137] [1] 1 [1437, 281, 2137] 70 C70
123) [3053, 393, 1213] [1] 1 [3053, 393, 1213] 70 C70
124) [281, 990, 24721] [1] 1 [281, 990, 24721] 70 C70
125) [281, 285, 11806] [1] 1 [281, 285, 11806] 70 C70
126) [37, 773, 135313] [1] 1 [37, 773, 135313] 70 C70
127) [37, 750, 125825] [1] 2 [37, 750, 125825] 140 C2 x C70
128) [37, 630, 70217] [1] 2 [37, 630, 70217] 140 C2 x C70
129) [37, 710, 120697] [1] 1 [37, 710, 120697] 70 C70
130) [37, 501, 34769] [1] 1 [37, 501, 34769] 70 C70
131) [536, 514, 1193] [1] 1 [536, 514, 1193] 70 C70
132) [28, 970, 37657] [1] 1 [28, 970, 37657] 70 C70
133) [28, 310, 21757] [1] 2 [28, 310, 21757] 140 C140
134) [28, 526, 43969] [1] 1 [28, 526, 43969] 70 C70
135) [581, 2781, 1842709] [1] 1 [581, 2781, 1842709] 70 C70
136) [617, 638, 12913] [1] 1 [617, 638, 12913] 70 C70
137) [1565, 229, 3329] [1] 1 [1565, 229, 3329] 140 C2 x C70
138) [33, 158, 4129] [2, 2] 1 [33, 158, 4129] 70 C70
139) [33, 158, 4129] [1] 1 [33, 158, 4129] 70 C70
140) [33, 446, 15937] [1] 1 [33, 446, 15937] 70 C70
141) [61, 665, 87361] [1] 1 [61, 665, 87361] 70 C70
142) [61, 881, 190609] [1] 1 [61, 881, 190609] 70 C70
143) [61, 201, 9353] [1] 1 [61, 201, 9353] 70 C70
144) [61, 725, 124681] [1] 1 [61, 725, 124681] 70 C70
145) [61, 518, 58297] [1] 1 [61, 518, 58297] 70 C70
146) [197, 137, 4249] [1] 1 [197, 137, 4249] 70 C70
147) [17, 894, 199384] [1] 1 [17, 894, 199384] 70 C70
148) [17, 899, 190996] [1] 1 [17, 899, 190996] 70 C70
149) [17, 1134, 315352] [1] 1 [17, 1134, 315352] 70 C70
150) [17, 1926, 612937] [1] 1 [17, 1926, 612937] 70 C70
151) [17, 685, 46582] [1] 1 [17, 685, 46582] 70 C70
152) [872, 198, 6313] [1] 1 [872, 198, 6313] 140 C140
153) [133, 177, 7001] [1] 1 [133, 177, 7001] 70 C70
154) [761, 101, 838] [1] 1 [761, 101, 838] 210 C210
155) [1016, 986, 14449] [1] 1 [1016, 986, 14449] 210 C210
156) [1165, 381, 1049] [1] 1 [1165, 381, 1049] 140 C2 x C70
157) [77, 837, 36061] [1] 1 [77, 837, 36061] 70 C70
158) [188, 698, 13513] [1] 1 [188, 698, 13513] 70 C70
159) [653, 73, 1169] [1] 1 [653, 73, 1169] 70 C70
160) [44, 598, 59657] [1] 2 [44, 598, 59657] 140 C2 x C70
161) [44, 770, 122881] [1] 1 [44, 770, 122881] 70 C70
162) [44, 974, 159553] [1] 1 [44, 974, 159553] 70 C70
163) [44, 534, 68473] [1] 1 [44, 534, 68473] 70 C70
164) [44, 202, 9497] [1] 1 [44, 202, 9497] 70 C70
165) [44, 1002, 35401] [1] 1 [44, 1002, 35401] 70 C70
166) [1985, 839, 64324] [1] 1 [1985, 839, 64324] 140 C140
167) [3161, 351, 11044] [1] 1 [3161, 351, 11044] 280 C280
168) [12, 550, 64825] [1] 2 [12, 550, 64825] 140 C2 x C70
169) [12, 466, 13921] [1] 1 [12, 466, 13921] 70 C70
170) [12, 542, 35809] [1] 1 [12, 542, 35809] 70 C70
171) [12, 658, 87073] [1] 2 [12, 658, 87073] 140 C2 x C70
172) [12, 766, 82741] [1] 2 [12, 766, 82741] 140 C2 x C70
173) [12, 590, 54577] [1] 1 [12, 590, 54577] 70 C70
174) [12, 506, 60937] [1] 1 [12, 506, 60937] 70 C70
175) [12, 1126, 247657] [1] 1 [12, 1126, 247657] 70 C70
176) [12, 994, 127009] [1] 1 [12, 994, 127009] 70 C70
177) [12, 1510, 550825] [1] 2 [12, 1510, 550825] 140 C2 x C70
178) [12, 334, 27589] [1] 2 [12, 334, 27589] 140 C2 x C70
179) [12, 530, 66337] [1] 1 [12, 530, 66337] 70 C70
180) [12, 662, 101449] [1] 1 [12, 662, 101449] 70 C70
181) [1385, 939, 4024] [1] 1 [1385, 939, 4024] 140 C140
182) [21, 614, 53593] [1] 1 [21, 614, 53593] 70 C70
183) [21, 913, 54877] [1] 1 [21, 913, 54877] 70 C70
184) [21, 970, 228421] [1] 1 [21, 970, 228421] 70 C70
185) [21, 286, 15073] [1] 1 [21, 286, 15073] 70 C70
186) [21, 565, 45361] [1] 1 [21, 565, 45361] 70 C70
187) [21, 949, 102253] [1] 1 [21, 949, 102253] 70 C70
188) [21, 758, 127177] [1] 1 [21, 758, 127177] 70 C70
189) [21, 442, 48757] [1] 1 [21, 442, 48757] 70 C70
190) [21, 905, 202441] [1] 1 [21, 905, 202441] 70 C70
191) [21, 334, 15793] [1] 1 [21, 334, 15793] 70 C70
192) [21, 241, 14473] [1] 1 [21, 241, 14473] 70 C70
193) [21, 295, 19861] [1] 2 [21, 295, 19861] 140 C2 x C70
194) [85, 437, 24601] [1] 1 [85, 437, 24601] 140 C140
195) [85, 201, 9569] [1] 1 [85, 201, 9569] 140 C140
196) [85, 581, 61249] [1] 1 [85, 581, 61249] 140 C140
197) [85, 566, 31129] [1] 1 [85, 566, 31129] 140 C140
198) [85, 369, 8009] [1] 1 [85, 369, 8009] 140 C2 x C70
199) [73, 157, 5998] [1] 1 [73, 157, 5998] 70 C70
200) [56, 1236, 376324] [1] 2 [56, 1236, 376324] 140 C2 x C70
201) [485, 561, 25209] [1] 2 [485, 561, 25209] 280 C2 x C2 x C70
202) [485, 1697, 718861] [1] 1 [485, 1697, 718861] 140 C140
203) [485, 1689, 710149] [1] 1 [485, 1689, 710149] 140 C2 x C70
204) [1193, 959, 12496] [1] 1 [1193, 959, 12496] 70 C70
205) [41, 723, 106072] [1] 1 [41, 723, 106072] 70 C70
206) [41, 1119, 152884] [1] 1 [41, 1119, 152884] 70 C70
207) [41, 277, 14662] [1] 1 [41, 277, 14662] 70 C70
208) [41, 927, 202276] [1] 1 [41, 927, 202276] 70 C70
209) [41, 1350, 413641] [1] 1 [41, 1350, 413641] 70 C70
210) [365, 926, 4129] [1] 1 [365, 926, 4129] 140 C2 x C70
211) [101, 593, 22237] [1] 1 [101, 593, 22237] 70 C70
212) [101, 629, 16873] [1] 1 [101, 629, 16873] 70 C70
213) [3433, 223, 4708] [1] 1 [3433, 223, 4708] 70 C70
214) [172, 518, 11353] [1] 1 [172, 518, 11353] 70 C70
215) [557, 721, 123137] [1] 1 [557, 721, 123137] 70 C70
216) [69, 422, 16921] [1] 1 [69, 422, 16921] 70 C70
217) [69, 686, 90049] [1] 1 [69, 686, 90049] 70 C70
218) [69, 157, 2281] [1] 1 [69, 157, 2281] 70 C70
219) [488, 1682, 702889] [1] 1 [488, 1682, 702889] 140 C140
220) [65, 258, 3901] [1] 1 [65, 258, 3901] 140 C140
221) [65, 1086, 119089] [1] 1 [65, 1086, 119089] 140 C2 x C70
222) [65, 742, 100201] [1] 1 [65, 742, 100201] 140 C140