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 168 Igusa CM invariants of non-normal (D4) fields: 210

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 358, 11753] [1] 1 [317, 358, 11753] 84 C2 x C42
2) [165, 133, 4381] [1] 1 [165, 133, 4381] 168 C2 x C84
3) [165, 461, 13489] [1] 1 [165, 461, 13489] 168 C2 x C84
4) [165, 521, 33169] [1] 1 [165, 521, 33169] 168 C2 x C2 x C42
5) [157, 133, 4069] [1] 1 [157, 133, 4069] 84 C84
6) [157, 317, 24769] [1] 1 [157, 317, 24769] 84 C2 x C42
7) [157, 409, 39897] [1] 1 [157, 409, 39897] 84 C2 x C42
8) [1397, 301, 5537] [1] 2 [1397, 301, 5537] 168 C2 x C2 x C42
9) [1749, 145, 1321] [1] 1 [1749, 145, 1321] 168 C2 x C84
10) [60, 602, 78841] [1] 2 [60, 602, 78841] 336 C2 x C2 x C84
11) [301, 509, 9913] [1] 1 [301, 509, 9913] 84 C84
12) [1208, 370, 4025] [1] 2 [1208, 370, 4025] 168 C2 x C2 x C42
13) [137, 206, 1841] [1] 1 [137, 206, 1841] 84 C84
14) [129, 222, 4065] [1] 1 [129, 222, 4065] 84 C2 x C42
15) [345, 302, 721] [1] 1 [345, 302, 721] 168 C2 x C84
16) [213, 605, 58225] [1] 2 [213, 605, 58225] 168 C2 x C84
17) [213, 293, 9481] [1] 1 [213, 293, 9481] 84 C84
18) [109, 533, 70777] [1] 1 [109, 533, 70777] 84 C84
19) [1317, 1642, 415909] [1] 1 [1317, 1642, 415909] 84 C2 x C42
20) [57, 518, 22393] [1] 2 [57, 518, 22393] 168 C2 x C84
21) [57, 270, 3633] [1] 1 [57, 270, 3633] 84 C2 x C42
22) [57, 270, 3633] [2, 2] 1 [57, 270, 3633] 84 C2 x C42
23) [205, 486, 6569] [1] 1 [205, 486, 6569] 168 C2 x C84
24) [309, 317, 18865] [7] 1 [309, 317, 18865] 12 C2 x C6
25) [685, 169, 6969] [1] 1 [685, 169, 6969] 168 C2 x C84
26) [136, 590, 42961] [1] 1 [136, 590, 42961] 168 C2 x C84
27) [136, 506, 33409] [1] 1 [136, 506, 33409] 168 C2 x C84
28) [136, 410, 40801] [1] 1 [136, 410, 40801] 168 C2 x C84
29) [253, 477, 3689] [1] 1 [253, 477, 3689] 84 C2 x C42
30) [253, 533, 24913] [1] 1 [253, 533, 24913] 84 C2 x C42
31) [13, 902, 201529] [1] 1 [13, 902, 201529] 84 C84
32) [13, 606, 81617] [1] 1 [13, 606, 81617] 84 C84
33) [13, 717, 105041] [1] 1 [13, 717, 105041] 84 C84
34) [76, 278, 9270] [1] 1 [76, 278, 9270] 84 C2 x C42
35) [76, 650, 94681] [1] 1 [76, 650, 94681] 84 C2 x C42
36) [76, 554, 32953] [1] 1 [76, 554, 32953] 84 C2 x C42
37) [8, 766, 146177] [1] 1 [8, 766, 146177] 84 C84
38) [8, 490, 59953] [1] 1 [8, 490, 59953] 84 C84
39) [8, 990, 244737] [1] 2 [8, 990, 244737] 168 C2 x C84
40) [8, 2038, 964633] [1] 1 [8, 2038, 964633] 84 C84
41) [8, 862, 179489] [1] 1 [8, 862, 179489] 84 C84
42) [8, 2838, 1489273] [1] 1 [8, 2838, 1489273] 84 C2 x C42
43) [8, 746, 130417] [1] 1 [8, 746, 130417] 84 C2 x C42
44) [8, 1006, 252977] [1] 1 [8, 1006, 252977] 84 C2 x C42
45) [8, 778, 150353] [1] 1 [8, 778, 150353] 84 C2 x C42
46) [8, 922, 212321] [1] 1 [8, 922, 212321] 84 C84
47) [8, 698, 121153] [1] 1 [8, 698, 121153] 84 C84
48) [8, 718, 113393] [1] 1 [8, 718, 113393] 84 C2 x C42
49) [8, 252, 14626] [1] 1 [8, 252, 14626] 84 C2 x C42
50) [8, 906, 203409] [1] 2 [8, 906, 203409] 168 C2 x C84
51) [8, 1718, 664153] [1] 1 [8, 1718, 664153] 84 C2 x C42
52) [8, 622, 75089] [1] 1 [8, 622, 75089] 84 C2 x C42
53) [8, 538, 56161] [1] 1 [8, 538, 56161] 84 C2 x C42
54) [8, 718, 105553] [1] 1 [8, 718, 105553] 84 C2 x C42
55) [5, 2201, 1121989] [1] 1 [5, 2201, 1121989] 84 C84
56) [5, 1749, 756949] [1] 1 [5, 1749, 756949] 84 C84
57) [5, 2634, 1649989] [1] 1 [5, 2634, 1649989] 84 C2 x C42
58) [5, 662, 108841] [1] 1 [5, 662, 108841] 84 C84
59) [5, 89, 1769] [13, 13] 1 [5, 89, 1769] 6 C6
60) [5, 292, 20191] [1] 1 [5, 292, 20191] 84 C2 x C42
61) [5, 2809, 1587589] [1] 1 [5, 2809, 1587589] 84 C84
62) [5, 2629, 1478149] [1] 1 [5, 2629, 1478149] 84 C2 x C42
63) [5, 2649, 1412389] [1] 1 [5, 2649, 1412389] 84 C84
64) [5, 1029, 229009] [1] 1 [5, 1029, 229009] 84 C2 x C42
65) [5, 1505, 555445] [1] 1 [5, 1505, 555445] 84 C2 x C42
66) [5, 301, 19649] [7, 7] 1 [5, 301, 19649] 12 C12
67) [5, 351, 28039] [1] 1 [5, 351, 28039] 84 C2 x C42
68) [5, 937, 217961] [1] 1 [5, 937, 217961] 84 C2 x C42
69) [5, 982, 241001] [1] 1 [5, 982, 241001] 84 C84
70) [29, 341, 23785] [1] 1 [29, 341, 23785] 84 C2 x C42
71) [29, 969, 234153] [1] 2 [29, 969, 234153] 168 C168
72) [29, 781, 137809] [1] 1 [29, 781, 137809] 84 C84
73) [29, 601, 68369] [1] 1 [29, 601, 68369] 84 C84
74) [29, 128, 3052] [1] 1 [29, 128, 3052] 84 C2 x C42
75) [29, 790, 155561] [1] 1 [29, 790, 155561] 84 C2 x C42
76) [29, 1209, 78313] [1] 1 [29, 1209, 78313] 84 C84
77) [29, 865, 184961] [1] 1 [29, 865, 184961] 84 C84
78) [92, 1302, 46969] [1] 1 [92, 1302, 46969] 84 C84
79) [193, 49, 166] [1] 1 [193, 49, 166] 84 C84
80) [93, 665, 96025] [1] 2 [93, 665, 96025] 168 C2 x C2 x C42
81) [93, 713, 114793] [1] 2 [93, 713, 114793] 168 C2 x C2 x C42
82) [93, 425, 43273] [1] 1 [93, 425, 43273] 84 C2 x C42
83) [93, 545, 48937] [1] 1 [93, 545, 48937] 84 C84
84) [24, 940, 220036] [1] 1 [24, 940, 220036] 84 C84
85) [24, 1126, 163369] [1] 1 [24, 1126, 163369] 84 C2 x C42
86) [24, 338, 26617] [1] 1 [24, 338, 26617] 84 C84
87) [24, 674, 98569] [1] 1 [24, 674, 98569] 84 C2 x C42
88) [877, 473, 6601] [1] 1 [877, 473, 6601] 84 C2 x C42
89) [428, 166, 5177] [1] 1 [428, 166, 5177] 84 C2 x C42
90) [428, 522, 6489] [1] 2 [428, 522, 6489] 168 C2 x C2 x C42
91) [141, 473, 22057] [1] 1 [141, 473, 22057] 84 C2 x C42
92) [141, 1594, 21013] [1] 1 [141, 1594, 21013] 84 C84
93) [152, 274, 6457] [1] 1 [152, 274, 6457] 84 C84
94) [152, 1194, 20641] [1] 1 [152, 1194, 20641] 84 C84
95) [40, 686, 111889] [1] 1 [40, 686, 111889] 168 C2 x C2 x C42
96) [40, 474, 31169] [1] 1 [40, 474, 31169] 168 C2 x C2 x C42
97) [40, 554, 67729] [1] 1 [40, 554, 67729] 168 C2 x C2 x C42
98) [1877, 85, 1337] [1] 1 [1877, 85, 1337] 84 C84
99) [908, 192, 8308] [1] 2 [908, 192, 8308] 168 C2 x C84
100) [509, 81, 1513] [1] 1 [509, 81, 1513] 84 C84
101) [185, 134, 1529] [1] 1 [185, 134, 1529] 168 C2 x C2 x C42
102) [185, 134, 1529] [2, 2] 1 [185, 134, 1529] 168 C2 x C2 x C42
103) [168, 250, 2017] [1] 1 [168, 250, 2017] 168 C2 x C84
104) [89, 72, 1207] [1] 1 [89, 72, 1207] 84 C2 x C42
105) [53, 361, 32249] [1] 1 [53, 361, 32249] 84 C2 x C42
106) [53, 502, 21449] [1] 1 [53, 502, 21449] 84 C84
107) [53, 957, 227889] [1] 2 [53, 957, 227889] 168 C168
108) [53, 265, 11713] [1] 1 [53, 265, 11713] 84 C2 x C42
109) [341, 541, 19889] [1] 1 [341, 541, 19889] 84 C84
110) [1821, 113, 2737] [1] 1 [1821, 113, 2737] 84 C2 x C42
111) [1909, 69, 713] [1] 1 [1909, 69, 713] 84 C84
112) [1253, 357, 6489] [1] 2 [1253, 357, 6489] 168 C2 x C2 x C42
113) [184, 930, 216041] [1] 1 [184, 930, 216041] 84 C84
114) [37, 713, 103033] [1] 1 [37, 713, 103033] 84 C2 x C42
115) [37, 481, 5809] [1] 1 [37, 481, 5809] 84 C84
116) [536, 66, 553] [1] 1 [536, 66, 553] 84 C2 x C42
117) [536, 658, 81977] [1] 1 [536, 658, 81977] 84 C2 x C42
118) [293, 210, 9853] [1] 1 [293, 210, 9853] 84 C84
119) [293, 565, 34025] [1] 2 [293, 565, 34025] 168 C168
120) [28, 518, 66073] [1] 1 [28, 518, 66073] 84 C2 x C42
121) [28, 806, 153337] [1] 1 [28, 806, 153337] 84 C84
122) [28, 722, 126289] [1] 1 [28, 722, 126289] 84 C2 x C42
123) [28, 602, 65401] [1] 1 [28, 602, 65401] 84 C2 x C42
124) [28, 154, 826] [1] 1 [28, 154, 826] 84 C2 x C42
125) [28, 750, 129425] [1] 2 [28, 750, 129425] 168 C2 x C2 x C42
126) [581, 209, 7289] [1] 1 [581, 209, 7289] 84 C2 x C42
127) [501, 749, 134113] [1] 1 [501, 749, 134113] 84 C2 x C42
128) [61, 749, 140113] [1] 1 [61, 749, 140113] 84 C84
129) [61, 830, 163441] [1] 1 [61, 830, 163441] 84 C84
130) [197, 301, 11569] [1] 1 [197, 301, 11569] 84 C84
131) [197, 558, 49473] [1] 2 [197, 558, 49473] 168 C2 x C84
132) [541, 533, 11377] [1] 1 [541, 533, 11377] 84 C84
133) [492, 650, 74137] [1] 1 [492, 650, 74137] 168 C2 x C84
134) [17, 550, 29657] [1] 1 [17, 550, 29657] 84 C84
135) [173, 246, 12361] [1] 1 [173, 246, 12361] 84 C84
136) [1589, 225, 9081] [1] 2 [1589, 225, 9081] 168 C2 x C84
137) [1589, 1194, 350053] [1] 1 [1589, 1194, 350053] 84 C84
138) [133, 421, 42681] [1] 1 [133, 421, 42681] 84 C2 x C42
139) [133, 413, 35161] [1] 1 [133, 413, 35161] 84 C84
140) [133, 645, 83225] [1] 2 [133, 645, 83225] 168 C2 x C84
141) [77, 505, 45257] [1] 1 [77, 505, 45257] 84 C2 x C42
142) [77, 565, 40825] [1] 2 [77, 565, 40825] 168 C2 x C84
143) [77, 670, 81425] [1] 2 [77, 670, 81425] 168 C2 x C84
144) [77, 406, 39977] [1] 1 [77, 406, 39977] 84 C2 x C42
145) [77, 294, 20377] [1] 1 [77, 294, 20377] 84 C2 x C42
146) [77, 533, 20953] [1] 1 [77, 533, 20953] 84 C84
147) [188, 186, 706] [1] 1 [188, 186, 706] 84 C2 x C42
148) [44, 466, 49889] [1] 1 [44, 466, 49889] 84 C2 x C42
149) [44, 2230, 172441] [1] 1 [44, 2230, 172441] 84 C84
150) [389, 257, 4745] [1] 1 [389, 257, 4745] 84 C2 x C42
151) [1292, 370, 29057] [1] 1 [1292, 370, 29057] 336 C2 x C168
152) [1157, 433, 39641] [1] 1 [1157, 433, 39641] 168 C168
153) [613, 201, 8721] [1] 1 [613, 201, 8721] 84 C2 x C42
154) [460, 102, 761] [1] 1 [460, 102, 761] 168 C2 x C2 x C42
155) [12, 722, 127969] [1] 1 [12, 722, 127969] 84 C2 x C42
156) [12, 842, 170329] [1] 1 [12, 842, 170329] 84 C2 x C42
157) [12, 698, 112393] [1] 1 [12, 698, 112393] 84 C2 x C42
158) [12, 866, 186289] [1] 1 [12, 866, 186289] 84 C2 x C42
159) [12, 758, 137833] [1] 1 [12, 758, 137833] 84 C2 x C42
160) [12, 1846, 352537] [1] 1 [12, 1846, 352537] 84 C2 x C42
161) [12, 1306, 156409] [1] 1 [12, 1306, 156409] 84 C2 x C42
162) [12, 674, 83569] [1] 1 [12, 674, 83569] 84 C2 x C42
163) [12, 370, 30337] [1] 1 [12, 370, 30337] 84 C2 x C42
164) [12, 490, 27577] [1] 1 [12, 490, 27577] 84 C2 x C42
165) [12, 830, 162817] [1] 1 [12, 830, 162817] 84 C2 x C42
166) [12, 638, 100993] [1] 1 [12, 638, 100993] 84 C2 x C42
167) [12, 686, 94417] [1] 1 [12, 686, 94417] 84 C2 x C42
168) [21, 178, 1852] [1] 1 [21, 178, 1852] 84 C84
169) [21, 950, 224281] [1] 1 [21, 950, 224281] 84 C2 x C42
170) [21, 1001, 250369] [1] 1 [21, 1001, 250369] 84 C2 x C42
171) [21, 1909, 172789] [1] 1 [21, 1909, 172789] 84 C2 x C42
172) [21, 509, 64513] [1] 1 [21, 509, 64513] 84 C84
173) [21, 749, 123193] [1] 1 [21, 749, 123193] 84 C84
174) [21, 854, 181993] [1] 1 [21, 854, 181993] 84 C84
175) [21, 749, 137473] [1] 1 [21, 749, 137473] 84 C2 x C42
176) [21, 461, 52705] [1] 1 [21, 461, 52705] 84 C2 x C42
177) [85, 641, 102529] [1] 1 [85, 641, 102529] 168 C2 x C84
178) [85, 469, 54969] [1] 1 [85, 469, 54969] 168 C2 x C84
179) [85, 557, 45241] [1] 1 [85, 557, 45241] 168 C2 x C84
180) [85, 617, 85801] [1] 1 [85, 617, 85801] 168 C2 x C2 x C42
181) [749, 137, 4505] [1] 1 [749, 137, 4505] 84 C2 x C42
182) [749, 505, 9641] [1] 1 [749, 505, 9641] 84 C2 x C42
183) [669, 509, 4393] [1] 1 [669, 509, 4393] 84 C2 x C42
184) [277, 369, 33417] [1] 2 [277, 369, 33417] 168 C2 x C2 x C42
185) [277, 665, 80017] [1] 2 [277, 665, 80017] 168 C2 x C2 x C42
186) [277, 373, 34713] [1] 1 [277, 373, 34713] 84 C2 x C42
187) [73, 178, 2008] [1] 1 [73, 178, 2008] 84 C2 x C42
188) [73, 315, 7268] [1] 1 [73, 315, 7268] 84 C84
189) [56, 546, 61929] [1] 2 [56, 546, 61929] 168 C2 x C2 x C42
190) [56, 750, 122481] [1] 2 [56, 750, 122481] 168 C2 x C2 x C42
191) [56, 478, 13217] [1] 1 [56, 478, 13217] 84 C84
192) [56, 526, 46769] [1] 1 [56, 526, 46769] 84 C84
193) [56, 1446, 164329] [1] 1 [56, 1446, 164329] 84 C84
194) [485, 229, 3289] [1] 1 [485, 229, 3289] 168 C2 x C84
195) [1797, 125, 3457] [1] 1 [1797, 125, 3457] 84 C84
196) [41, 258, 14632] [1] 1 [41, 258, 14632] 84 C2 x C42
197) [353, 186, 8296] [1] 1 [353, 186, 8296] 84 C2 x C42
198) [101, 377, 24397] [1] 1 [101, 377, 24397] 84 C84
199) [101, 609, 74313] [1] 2 [101, 609, 74313] 168 C2 x C84
200) [381, 1957, 392725] [1] 1 [381, 1957, 392725] 84 C2 x C42
201) [381, 254, 10033] [1] 1 [381, 254, 10033] 84 C84
202) [69, 569, 66433] [1] 1 [69, 569, 66433] 84 C84
203) [69, 817, 17677] [1] 1 [69, 817, 17677] 84 C2 x C42
204) [69, 470, 54121] [1] 1 [69, 470, 54121] 84 C84
205) [69, 569, 36073] [1] 1 [69, 569, 36073] 84 C84
206) [69, 709, 18013] [1] 1 [69, 709, 18013] 84 C84
207) [69, 701, 118969] [1] 1 [69, 701, 118969] 84 C84
208) [1084, 410, 3001] [1] 1 [1084, 410, 3001] 84 C84
209) [989, 445, 7721] [1] 1 [989, 445, 7721] 84 C2 x C42
210) [444, 134, 2713] [1] 1 [444, 134, 2713] 168 C2 x C2 x C42