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 56 Igusa CM invariants of non-normal (D4) fields: 207

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 501, 4977] [1] 2 [317, 501, 4977] 56 C2 x C28
2) [1529, 443, 18100] [1] 1 [1529, 443, 18100] 28 C28
3) [1605, 221, 11809] [1] 1 [1605, 221, 11809] 56 C2 x C28
4) [60, 112, 1636] [1] 1 [60, 112, 1636] 56 C2 x C28
5) [60, 386, 2689] [1] 1 [60, 386, 2689] 56 C2 x C2 x C14
6) [236, 922, 204025] [1] 1 [236, 922, 204025] 28 C28
7) [120, 386, 2569] [1] 1 [120, 386, 2569] 56 C2 x C28
8) [120, 556, 19204] [1] 1 [120, 556, 19204] 56 C2 x C28
9) [120, 654, 37809] [1] 1 [120, 654, 37809] 56 C2 x C28
10) [1128, 302, 4753] [1] 1 [1128, 302, 4753] 56 C2 x C28
11) [296, 414, 32193] [1] 2 [296, 414, 32193] 112 C2 x C2 x C28
12) [104, 90, 1921] [1] 1 [104, 90, 1921] 56 C2 x C2 x C14
13) [109, 425, 15481] [1] 1 [109, 425, 15481] 28 C28
14) [109, 473, 26257] [1] 2 [109, 473, 26257] 56 C2 x C28
15) [109, 449, 8953] [1] 1 [109, 449, 8953] 28 C28
16) [97, 44, 387] [1] 1 [97, 44, 387] 28 C28
17) [97, 161, 3546] [1] 1 [97, 161, 3546] 28 C28
18) [1317, 365, 32977] [1] 1 [1317, 365, 32977] 28 C28
19) [205, 178, 541] [1] 1 [205, 178, 541] 56 C2 x C28
20) [205, 101, 2089] [1] 1 [205, 101, 2089] 56 C2 x C28
21) [1752, 146, 3577] [1] 1 [1752, 146, 3577] 112 C2 x C56
22) [380, 158, 161] [1] 1 [380, 158, 161] 56 C2 x C28
23) [380, 246, 1449] [1] 2 [380, 246, 1449] 112 C2 x C2 x C28
24) [876, 344, 21700] [1] 1 [876, 344, 21700] 112 C2 x C56
25) [253, 893, 198793] [1] 1 [253, 893, 198793] 28 C28
26) [13, 69, 641] [5, 5] 1 [13, 69, 641] 7 C7
27) [13, 561, 32657] [1] 2 [13, 561, 32657] 56 C2 x C28
28) [13, 445, 42925] [1] 2 [13, 445, 42925] 56 C2 x C28
29) [13, 473, 43033] [1] 1 [13, 473, 43033] 28 C28
30) [13, 405, 37025] [1] 2 [13, 405, 37025] 56 C56
31) [13, 321, 8441] [1] 1 [13, 321, 8441] 28 C28
32) [13, 545, 49657] [1] 1 [13, 545, 49657] 28 C2 x C14
33) [13, 905, 204025] [1] 2 [13, 905, 204025] 56 C56
34) [13, 510, 24257] [1] 1 [13, 510, 24257] 28 C28
35) [13, 497, 61489] [1] 1 [13, 497, 61489] 28 C28
36) [76, 338, 3937] [1] 1 [76, 338, 3937] 28 C2 x C14
37) [636, 506, 409] [1] 1 [636, 506, 409] 56 C2 x C2 x C14
38) [8, 606, 50337] [1] 2 [8, 606, 50337] 56 C2 x C2 x C14
39) [8, 522, 59409] [1] 2 [8, 522, 59409] 56 C2 x C2 x C14
40) [8, 250, 8897] [1] 1 [8, 250, 8897] 28 C2 x C14
41) [8, 606, 84609] [1] 2 [8, 606, 84609] 56 C2 x C2 x C14
42) [8, 222, 11929] [1] 2 [8, 222, 11929] 56 C2 x C28
43) [8, 626, 97897] [1] 1 [8, 626, 97897] 28 C28
44) [8, 136, 3166] [1] 1 [8, 136, 3166] 28 C28
45) [8, 442, 46529] [1] 2 [8, 442, 46529] 56 C2 x C2 x C14
46) [8, 786, 88201] [1] 1 [8, 786, 88201] 28 C28
47) [8, 658, 96073] [1] 1 [8, 658, 96073] 28 C28
48) [8, 298, 19313] [1] 1 [8, 298, 19313] 28 C2 x C14
49) [8, 114, 1897] [7] 1 [8, 114, 1897] 4 C4
50) [8, 598, 86809] [1] 1 [8, 598, 86809] 28 C28
51) [8, 498, 48553] [1] 1 [8, 498, 48553] 28 C28
52) [8, 638, 66913] [1] 2 [8, 638, 66913] 56 C2 x C28
53) [8, 558, 70641] [1] 2 [8, 558, 70641] 56 C2 x C28
54) [5, 721, 127429] [1] 1 [5, 721, 127429] 28 C28
55) [5, 749, 117469] [1] 1 [5, 749, 117469] 28 C2 x C14
56) [5, 641, 102709] [1] 1 [5, 641, 102709] 28 C28
57) [5, 846, 176049] [1] 2 [5, 846, 176049] 56 C2 x C28
58) [5, 921, 209529] [1] 2 [5, 921, 209529] 56 C2 x C28
59) [5, 646, 90809] [1] 1 [5, 646, 90809] 28 C28
60) [5, 721, 129809] [1] 1 [5, 721, 129809] 28 C28
61) [5, 1057, 234661] [1] 2 [5, 1057, 234661] 56 C56
62) [5, 849, 173169] [1] 2 [5, 849, 173169] 56 C2 x C28
63) [5, 526, 65249] [1] 1 [5, 526, 65249] 28 C28
64) [5, 521, 57049] [1] 1 [5, 521, 57049] 28 C28
65) [5, 329, 23809] [1] 1 [5, 329, 23809] 28 C28
66) [5, 801, 159849] [1] 2 [5, 801, 159849] 56 C56
67) [5, 569, 72329] [1] 1 [5, 569, 72329] 28 C28
68) [5, 558, 66321] [1] 2 [5, 558, 66321] 56 C56
69) [5, 649, 85769] [1] 1 [5, 649, 85769] 28 C28
70) [5, 493, 58001] [1] 1 [5, 493, 58001] 28 C28
71) [5, 589, 81449] [1] 1 [5, 589, 81449] 28 C28
72) [5, 477, 55521] [1] 2 [5, 477, 55521] 56 C2 x C28
73) [5, 702, 105201] [1] 2 [5, 702, 105201] 56 C56
74) [5, 609, 87109] [1] 1 [5, 609, 87109] 28 C28
75) [5, 438, 39961] [1] 1 [5, 438, 39961] 28 C28
76) [5, 889, 196049] [1] 2 [5, 889, 196049] 56 C56
77) [5, 333, 23941] [1] 1 [5, 333, 23941] 28 C28
78) [5, 566, 79369] [1] 1 [5, 566, 79369] 28 C28
79) [5, 429, 45649] [1] 1 [5, 429, 45649] 28 C28
80) [5, 717, 127161] [1] 2 [5, 717, 127161] 56 C2 x C28
81) [5, 654, 88929] [1] 2 [5, 654, 88929] 56 C2 x C28
82) [5, 909, 206289] [1] 2 [5, 909, 206289] 56 C56
83) [5, 569, 73909] [1] 1 [5, 569, 73909] 28 C28
84) [5, 393, 35101] [1] 1 [5, 393, 35101] 28 C28
85) [5, 257, 15961] [1] 1 [5, 257, 15961] 28 C28
86) [5, 553, 69041] [1] 2 [5, 553, 69041] 56 C56
87) [5, 301, 21289] [1] 1 [5, 301, 21289] 28 C28
88) [5, 822, 162441] [1] 2 [5, 822, 162441] 56 C56
89) [5, 709, 117469] [1] 1 [5, 709, 117469] 28 C2 x C14
90) [5, 626, 89149] [1] 1 [5, 626, 89149] 28 C28
91) [5, 449, 43369] [1] 1 [5, 449, 43369] 28 C28
92) [5, 834, 157069] [1] 1 [5, 834, 157069] 28 C2 x C14
93) [5, 541, 71969] [1] 1 [5, 541, 71969] 28 C28
94) [5, 473, 48901] [1] 1 [5, 473, 48901] 28 C28
95) [29, 645, 98721] [1] 2 [29, 645, 98721] 56 C2 x C28
96) [29, 301, 7969] [1] 1 [29, 301, 7969] 28 C28
97) [29, 465, 46161] [1] 2 [29, 465, 46161] 56 C2 x C28
98) [29, 142, 4577] [1] 1 [29, 142, 4577] 28 C28
99) [29, 549, 34569] [1] 2 [29, 549, 34569] 56 C2 x C28
100) [92, 270, 4977] [1] 2 [92, 270, 4977] 56 C2 x C2 x C14
101) [92, 240, 6948] [1] 2 [92, 240, 6948] 56 C2 x C28
102) [92, 176, 3236] [1] 1 [92, 176, 3236] 28 C28
103) [440, 92, 356] [1] 1 [440, 92, 356] 56 C2 x C28
104) [93, 465, 28737] [1] 1 [93, 465, 28737] 28 C28
105) [933, 473, 16513] [1] 1 [933, 473, 16513] 28 C28
106) [933, 649, 77077] [1] 2 [933, 649, 77077] 56 C2 x C2 x C14
107) [933, 285, 1413] [1] 1 [933, 285, 1413] 28 C28
108) [24, 398, 11857] [1] 1 [24, 398, 11857] 28 C2 x C14
109) [24, 386, 7849] [1] 1 [24, 386, 7849] 28 C2 x C14
110) [24, 290, 12361] [1] 1 [24, 290, 12361] 28 C2 x C14
111) [24, 508, 48292] [1] 1 [24, 508, 48292] 28 C28
112) [221, 97, 2297] [1] 1 [221, 97, 2297] 56 C2 x C28
113) [221, 61, 433] [1] 1 [221, 61, 433] 56 C2 x C28
114) [221, 633, 95697] [1] 2 [221, 633, 95697] 112 C4 x C28
115) [257, 298, 1384] [1] 1 [257, 298, 1384] 84 C84
116) [893, 465, 3825] [1] 4 [893, 465, 3825] 112 C2 x C2 x C28
117) [428, 610, 50225] [1] 2 [428, 610, 50225] 56 C2 x C28
118) [408, 510, 6273] [1] 1 [408, 510, 6273] 56 C2 x C28
119) [40, 436, 34564] [1] 1 [40, 436, 34564] 56 C56
120) [149, 638, 92225] [1] 1 [149, 638, 92225] 28 C2 x C14
121) [956, 430, 11809] [1] 1 [956, 430, 11809] 28 C28
122) [509, 333, 12325] [1] 1 [509, 333, 12325] 28 C28
123) [113, 350, 14353] [1] 1 [113, 350, 14353] 28 C28
124) [248, 92, 1124] [1] 1 [248, 92, 1124] 28 C28
125) [1660, 186, 2009] [1] 1 [1660, 186, 2009] 56 C2 x C28
126) [156, 58, 217] [1] 1 [156, 58, 217] 56 C2 x C28
127) [156, 656, 10084] [1] 1 [156, 656, 10084] 56 C2 x C28
128) [53, 486, 4777] [1] 1 [53, 486, 4777] 28 C28
129) [53, 453, 36873] [1] 2 [53, 453, 36873] 56 C2 x C28
130) [53, 289, 15037] [1] 1 [53, 289, 15037] 28 C28
131) [53, 181, 7117] [1] 1 [53, 181, 7117] 28 C28
132) [1941, 53, 217] [1] 1 [1941, 53, 217] 28 C28
133) [341, 310, 2201] [1] 1 [341, 310, 2201] 28 C28
134) [1052, 390, 153] [1] 2 [1052, 390, 153] 56 C2 x C28
135) [184, 494, 1393] [1] 1 [184, 494, 1393] 28 C2 x C14
136) [37, 337, 4333] [1] 1 [37, 337, 4333] 28 C28
137) [28, 126, 2177] [1] 1 [28, 126, 2177] 28 C2 x C14
138) [28, 192, 5828] [1] 1 [28, 192, 5828] 28 C2 x C14
139) [28, 470, 30025] [1] 2 [28, 470, 30025] 56 C2 x C28
140) [28, 506, 14617] [1] 1 [28, 506, 14617] 28 C2 x C14
141) [581, 513, 1737] [1] 2 [581, 513, 1737] 56 C2 x C28
142) [581, 417, 18925] [1] 1 [581, 417, 18925] 28 C28
143) [204, 242, 13825] [1] 1 [204, 242, 13825] 56 C2 x C28
144) [617, 279, 796] [1] 1 [617, 279, 796] 28 C28
145) [61, 249, 5969] [1] 1 [61, 249, 5969] 28 C28
146) [61, 309, 2993] [1] 1 [61, 309, 2993] 28 C28
147) [1085, 49, 329] [1] 1 [1085, 49, 329] 56 C2 x C28
148) [1461, 269, 193] [1] 1 [1461, 269, 193] 28 C28
149) [17, 258, 8413] [1] 1 [17, 258, 8413] 28 C28
150) [17, 1023, 251428] [1] 1 [17, 1023, 251428] 28 C28
151) [456, 110, 1201] [1] 1 [456, 110, 1201] 56 C2 x C2 x C14
152) [1037, 501, 60417] [1] 2 [1037, 501, 60417] 112 C2 x C56
153) [1644, 346, 23353] [1] 1 [1644, 346, 23353] 56 C2 x C2 x C14
154) [232, 164, 5796] [1] 1 [232, 164, 5796] 56 C2 x C2 x C14
155) [133, 413, 6433] [1] 1 [133, 413, 6433] 28 C28
156) [680, 58, 161] [1] 1 [680, 58, 161] 112 C2 x C2 x C28
157) [77, 105, 2737] [1] 1 [77, 105, 2737] 28 C2 x C14
158) [569, 171, 340] [1] 1 [569, 171, 340] 28 C28
159) [188, 170, 457] [1] 1 [188, 170, 457] 28 C28
160) [653, 206, 161] [1] 1 [653, 206, 161] 28 C28
161) [44, 354, 17073] [1] 2 [44, 354, 17073] 56 C2 x C2 x C14
162) [44, 510, 8001] [1] 2 [44, 510, 8001] 56 C2 x C2 x C14
163) [44, 1080, 185956] [1] 1 [44, 1080, 185956] 28 C28
164) [44, 486, 19449] [1] 2 [44, 486, 19449] 56 C2 x C28
165) [44, 86, 1673] [1] 1 [44, 86, 1673] 28 C2 x C14
166) [12, 218, 7081] [1] 1 [12, 218, 7081] 28 C2 x C14
167) [12, 58, 814] [1] 1 [12, 58, 814] 28 C2 x C14
168) [12, 382, 22609] [1] 1 [12, 382, 22609] 28 C2 x C14
169) [12, 602, 52969] [1] 2 [12, 602, 52969] 56 C2 x C2 x C14
170) [12, 106, 1486] [1] 1 [12, 106, 1486] 28 C2 x C14
171) [12, 730, 44473] [1] 1 [12, 730, 44473] 28 C2 x C14
172) [12, 58, 478] [1] 1 [12, 58, 478] 28 C2 x C14
173) [12, 58, 598] [1] 1 [12, 58, 598] 28 C2 x C14
174) [12, 202, 3289] [1] 1 [12, 202, 3289] 28 C2 x C14
175) [12, 58, 334] [1] 1 [12, 58, 334] 28 C2 x C14
176) [12, 370, 18673] [1] 1 [12, 370, 18673] 28 C2 x C14
177) [12, 526, 39169] [1] 1 [12, 526, 39169] 28 C2 x C14
178) [12, 670, 59953] [1] 1 [12, 670, 59953] 28 C2 x C14
179) [12, 454, 23881] [1] 1 [12, 454, 23881] 28 C2 x C14
180) [12, 886, 56281] [1] 1 [12, 886, 56281] 28 C2 x C14
181) [12, 430, 28897] [1] 1 [12, 430, 28897] 28 C2 x C14
182) [21, 350, 29281] [1] 1 [21, 350, 29281] 28 C2 x C14
183) [21, 449, 19273] [1] 1 [21, 449, 19273] 28 C28
184) [21, 470, 33721] [1] 1 [21, 470, 33721] 28 C28
185) [21, 329, 19873] [1] 1 [21, 329, 19873] 28 C2 x C14
186) [21, 173, 7057] [1] 1 [21, 173, 7057] 28 C28
187) [21, 581, 37009] [1] 1 [21, 581, 37009] 28 C2 x C14
188) [21, 401, 33769] [1] 1 [21, 401, 33769] 28 C28
189) [21, 518, 18697] [1] 1 [21, 518, 18697] 28 C28
190) [21, 485, 46201] [1] 1 [21, 485, 46201] 28 C2 x C14
191) [21, 169, 3313] [1] 1 [21, 169, 3313] 28 C28
192) [21, 497, 10297] [1] 1 [21, 497, 10297] 28 C28
193) [21, 541, 15289] [1] 1 [21, 541, 15289] 28 C28
194) [85, 326, 14329] [1] 1 [85, 326, 14329] 56 C2 x C28
195) [85, 157, 5121] [1] 1 [85, 157, 5121] 56 C56
196) [73, 160, 487] [1] 1 [73, 160, 487] 28 C28
197) [56, 420, 11844] [1] 2 [56, 420, 11844] 56 C2 x C2 x C14
198) [56, 306, 10809] [1] 2 [56, 306, 10809] 56 C2 x C28
199) [56, 876, 51844] [2, 2] 1 [56, 876, 51844] 14 C14
200) [284, 490, 4361] [1] 2 [284, 490, 4361] 56 C2 x C2 x C14
201) [353, 327, 1228] [1] 1 [353, 327, 1228] 28 C28
202) [172, 392, 29988] [1] 2 [172, 392, 29988] 56 C2 x C2 x C14
203) [172, 88, 388] [1] 1 [172, 88, 388] 28 C28
204) [557, 525, 7497] [1] 4 [557, 525, 7497] 112 C2 x C2 x C28
205) [69, 161, 6049] [1] 1 [69, 161, 6049] 28 C2 x C14
206) [65, 139, 2084] [1] 1 [65, 139, 2084] 56 C56
207) [1309, 329, 553] [1] 1 [1309, 329, 553] 56 C2 x C28