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 336 Igusa CM invariants of non-normal (D4) fields: 145

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [3541, 277, 18297] [1] 1 [3541, 277, 18297] 168 C168
2) [317, 313, 18073] [1] 1 [317, 313, 18073] 168 C2 x C84
3) [165, 761, 129889] [1] 1 [165, 761, 129889] 336 C2 x C168
4) [165, 277, 15841] [1] 1 [165, 277, 15841] 336 C4 x C84
5) [165, 417, 42441] [1] 1 [165, 417, 42441] 336 C2 x C2 x C84
6) [165, 662, 99001] [1] 1 [165, 662, 99001] 336 C4 x C84
7) [165, 629, 73129] [1] 1 [165, 629, 73129] 336 C4 x C84
8) [1829, 109, 2513] [1] 1 [1829, 109, 2513] 168 C168
9) [437, 405, 35653] [1] 1 [437, 405, 35653] 168 C2 x C84
10) [60, 806, 150649] [1] 1 [60, 806, 150649] 336 C2 x C2 x C84
11) [60, 482, 42721] [1] 1 [60, 482, 42721] 336 C2 x C2 x C84
12) [60, 794, 151609] [1] 1 [60, 794, 151609] 336 C2 x C2 x C84
13) [60, 746, 136969] [1] 1 [60, 746, 136969] 336 C2 x C2 x C84
14) [229, 689, 93433] [1] 1 [229, 689, 93433] 504 C3 x C168
15) [88, 334, 27537] [1] 1 [88, 334, 27537] 168 C2 x C84
16) [120, 626, 77689] [1] 1 [120, 626, 77689] 336 C2 x C2 x C84
17) [429, 725, 113281] [1] 1 [429, 725, 113281] 336 C2 x C168
18) [357, 581, 37177] [1] 1 [357, 581, 37177] 336 C2 x C2 x C84
19) [104, 286, 16705] [1] 1 [104, 286, 16705] 336 C4 x C84
20) [104, 458, 52337] [1] 1 [104, 458, 52337] 336 C2 x C2 x C84
21) [161, 182, 5705] [1] 1 [161, 182, 5705] 168 C2 x C84
22) [312, 338, 25753] [1] 1 [312, 338, 25753] 336 C4 x C84
23) [813, 241, 14317] [1] 1 [813, 241, 14317] 168 C168
24) [348, 326, 25177] [1] 1 [348, 326, 25177] 336 C2 x C168
25) [1384, 314, 12193] [1] 1 [1384, 314, 12193] 1008 C2 x C6 x C84
26) [1501, 261, 7649] [1] 1 [1501, 261, 7649] 168 C168
27) [209, 478, 3617] [1] 1 [209, 478, 3617] 168 C168
28) [1005, 461, 22729] [1] 1 [1005, 461, 22729] 336 C2 x C2 x C84
29) [13, 990, 244817] [1] 1 [13, 990, 244817] 168 C168
30) [13, 918, 210473] [1] 1 [13, 918, 210473] 168 C168
31) [220, 626, 66289] [1] 1 [220, 626, 66289] 336 C2 x C2 x C2 x C42
32) [76, 698, 110857] [1] 1 [76, 698, 110857] 168 C2 x C84
33) [8, 958, 228641] [1] 1 [8, 958, 228641] 168 C2 x C84
34) [8, 938, 218161] [1] 1 [8, 938, 218161] 168 C2 x C84
35) [280, 446, 39649] [1] 1 [280, 446, 39649] 336 C2 x C2 x C2 x C42
36) [1784, 130, 2441] [1] 1 [1784, 130, 2441] 168 C168
37) [29, 853, 176617] [1] 1 [29, 853, 176617] 168 C2 x C84
38) [92, 286, 18977] [1] 1 [92, 286, 18977] 168 C2 x C84
39) [1693, 129, 3737] [1] 1 [1693, 129, 3737] 168 C168
40) [780, 506, 14089] [1] 1 [780, 506, 14089] 672 C2 x C2 x C2 x C84
41) [589, 725, 130081] [1] 1 [589, 725, 130081] 168 C168
42) [24, 1010, 255001] [1] 1 [24, 1010, 255001] 168 C2 x C84
43) [24, 706, 119209] [1] 1 [24, 706, 119209] 168 C2 x C2 x C42
44) [24, 914, 208633] [1] 1 [24, 914, 208633] 168 C2 x C2 x C42
45) [221, 649, 76073] [1] 1 [221, 649, 76073] 336 C2 x C2 x C84
46) [221, 361, 28105] [1] 1 [221, 361, 28105] 336 C2 x C2 x C84
47) [221, 497, 57277] [1] 1 [221, 497, 57277] 336 C4 x C84
48) [413, 553, 21833] [1] 1 [413, 553, 21833] 168 C168
49) [285, 365, 32665] [1] 1 [285, 365, 32665] 336 C4 x C84
50) [285, 569, 36409] [1] 1 [285, 569, 36409] 336 C2 x C168
51) [781, 489, 3353] [1] 1 [781, 489, 3353] 168 C2 x C84
52) [893, 493, 23033] [1] 1 [893, 493, 23033] 168 C2 x C84
53) [141, 809, 153433] [1] 1 [141, 809, 153433] 168 C2 x C84
54) [141, 385, 34201] [1] 1 [141, 385, 34201] 168 C2 x C84
55) [141, 941, 220489] [1] 1 [141, 941, 220489] 168 C168
56) [952, 450, 3977] [1] 1 [952, 450, 3977] 336 C4 x C84
57) [1093, 417, 10409] [1] 1 [1093, 417, 10409] 840 C840
58) [40, 654, 90929] [1] 1 [40, 654, 90929] 336 C2 x C2 x C84
59) [40, 606, 64769] [1] 1 [40, 606, 64769] 336 C2 x C2 x C84
60) [728, 146, 4601] [1] 1 [728, 146, 4601] 336 C2 x C2 x C84
61) [149, 342, 26857] [1] 1 [149, 342, 26857] 168 C168
62) [149, 694, 110873] [1] 1 [149, 694, 110873] 168 C2 x C84
63) [1541, 241, 4889] [1] 1 [1541, 241, 4889] 168 C168
64) [140, 230, 12665] [1] 1 [140, 230, 12665] 336 C4 x C84
65) [140, 410, 39785] [1] 1 [140, 410, 39785] 336 C4 x C84
66) [140, 646, 76889] [1] 1 [140, 646, 76889] 336 C2 x C168
67) [140, 386, 32209] [1] 1 [140, 386, 32209] 336 C2 x C2 x C2 x C42
68) [1704, 170, 5521] [1] 1 [1704, 170, 5521] 336 C2 x C168
69) [248, 290, 8873] [1] 1 [248, 290, 8873] 168 C168
70) [168, 602, 62209] [1] 1 [168, 602, 62209] 336 C2 x C2 x C84
71) [89, 763, 33380] [1] 1 [89, 763, 33380] 168 C168
72) [744, 138, 4017] [1] 1 [744, 138, 4017] 336 C4 x C84
73) [533, 377, 34333] [1] 1 [533, 377, 34333] 336 C4 x C84
74) [53, 790, 142457] [1] 1 [53, 790, 142457] 168 C2 x C84
75) [53, 517, 54089] [1] 1 [53, 517, 54089] 168 C168
76) [53, 1382, 374873] [1] 1 [53, 1382, 374873] 168 C168
77) [53, 701, 102697] [1] 1 [53, 701, 102697] 168 C2 x C84
78) [568, 578, 37513] [1] 1 [568, 578, 37513] 504 C2 x C6 x C42
79) [341, 317, 20945] [1] 1 [341, 317, 20945] 168 C2 x C84
80) [332, 474, 54841] [1] 1 [332, 474, 54841] 168 C168
81) [332, 274, 6817] [1] 1 [332, 274, 6817] 168 C2 x C84
82) [184, 394, 23905] [1] 1 [184, 394, 23905] 168 C2 x C84
83) [37, 981, 240137] [1] 1 [37, 981, 240137] 168 C168
84) [37, 549, 69569] [1] 1 [37, 549, 69569] 168 C168
85) [37, 741, 132377] [1] 1 [37, 741, 132377] 168 C168
86) [949, 465, 13961] [1] 1 [949, 465, 13961] 336 C2 x C2 x C84
87) [293, 461, 47197] [1] 1 [293, 461, 47197] 168 C168
88) [28, 950, 224617] [1] 1 [28, 950, 224617] 168 C168
89) [28, 702, 101249] [1] 1 [28, 702, 101249] 168 C2 x C84
90) [28, 938, 218953] [1] 1 [28, 938, 218953] 168 C2 x C2 x C42
91) [445, 537, 13241] [1] 1 [445, 537, 13241] 672 C2 x C336
92) [581, 217, 10465] [1] 1 [581, 217, 10465] 168 C2 x C2 x C42
93) [316, 374, 23593] [1] 1 [316, 374, 23593] 504 C3 x C168
94) [508, 762, 143129] [1] 1 [508, 762, 143129] 168 C2 x C84
95) [501, 593, 42697] [1] 1 [501, 593, 42697] 168 C168
96) [617, 806, 152537] [1] 1 [617, 806, 152537] 168 C168
97) [1677, 185, 8137] [1] 1 [1677, 185, 8137] 672 C2 x C2 x C168
98) [197, 401, 38969] [1] 1 [197, 401, 38969] 168 C2 x C84
99) [597, 545, 20377] [1] 1 [597, 545, 20377] 168 C2 x C84
100) [492, 234, 5817] [1] 1 [492, 234, 5817] 336 C4 x C84
101) [1661, 193, 8897] [1] 1 [1661, 193, 8897] 168 C2 x C84
102) [664, 530, 16441] [1] 1 [664, 530, 16441] 168 C2 x C84
103) [664, 178, 7257] [1] 1 [664, 178, 7257] 168 C2 x C84
104) [17, 478, 39713] [1] 1 [17, 478, 39713] 168 C168
105) [17, 446, 48641] [1] 1 [17, 446, 48641] 168 C168
106) [373, 270, 12257] [1] 1 [373, 270, 12257] 168 C2 x C84
107) [645, 697, 120001] [1] 1 [645, 697, 120001] 336 C4 x C84
108) [997, 145, 3013] [1] 1 [997, 145, 3013] 168 C168
109) [2789, 593, 3545] [1] 1 [2789, 593, 3545] 168 C168
110) [181, 361, 27105] [1] 1 [181, 361, 27105] 168 C2 x C2 x C42
111) [869, 505, 27041] [1] 1 [869, 505, 27041] 168 C2 x C84
112) [133, 630, 65177] [1] 1 [133, 630, 65177] 168 C168
113) [133, 917, 207529] [1] 1 [133, 917, 207529] 168 C2 x C84
114) [3389, 349, 22825] [1] 1 [3389, 349, 22825] 168 C168
115) [77, 805, 155057] [1] 1 [77, 805, 155057] 168 C2 x C84
116) [77, 677, 114409] [1] 1 [77, 677, 114409] 168 C168
117) [77, 901, 199697] [1] 1 [77, 901, 199697] 168 C168
118) [620, 514, 4049] [1] 1 [620, 514, 4049] 336 C2 x C2 x C84
119) [44, 418, 42097] [1] 1 [44, 418, 42097] 168 C2 x C84
120) [44, 458, 51737] [1] 1 [44, 458, 51737] 168 C2 x C84
121) [44, 694, 99113] [1] 1 [44, 694, 99113] 168 C2 x C84
122) [389, 313, 23617] [1] 1 [389, 313, 23617] 168 C2 x C84
123) [613, 189, 8777] [1] 1 [613, 189, 8777] 168 C168
124) [12, 766, 131137] [1] 1 [12, 766, 131137] 168 C2 x C84
125) [21, 901, 201769] [1] 1 [21, 901, 201769] 168 C168
126) [21, 649, 101473] [1] 1 [21, 649, 101473] 168 C2 x C84
127) [21, 917, 209041] [1] 1 [21, 917, 209041] 168 C168
128) [277, 349, 27057] [1] 1 [277, 349, 27057] 168 C2 x C84
129) [741, 141, 4785] [1] 1 [741, 141, 4785] 336 C2 x C2 x C84
130) [56, 322, 24521] [1] 1 [56, 322, 24521] 168 C2 x C2 x C42
131) [56, 574, 81473] [1] 1 [56, 574, 81473] 168 C2 x C2 x C42
132) [56, 574, 44513] [1] 1 [56, 574, 44513] 168 C2 x C84
133) [56, 466, 53785] [1] 1 [56, 466, 53785] 168 C2 x C84
134) [56, 946, 222329] [1] 1 [56, 946, 222329] 168 C168
135) [1036, 434, 9793] [1] 1 [1036, 434, 9793] 336 C2 x C2 x C2 x C42
136) [485, 269, 17969] [1] 1 [485, 269, 17969] 336 C4 x C84
137) [41, 422, 43865] [1] 1 [41, 422, 43865] 168 C2 x C84
138) [812, 490, 8057] [1] 1 [812, 490, 8057] 336 C2 x C2 x C2 x C42
139) [101, 661, 93449] [1] 1 [101, 661, 93449] 168 C2 x C84
140) [101, 545, 63121] [1] 1 [101, 545, 63121] 168 C2 x C84
141) [101, 421, 42265] [1] 1 [101, 421, 42265] 168 C2 x C84
142) [717, 521, 16057] [1] 1 [717, 521, 16057] 168 C168
143) [69, 713, 126937] [1] 1 [69, 713, 126937] 168 C2 x C84
144) [69, 905, 201841] [1] 1 [69, 905, 201841] 168 C2 x C84
145) [444, 514, 2113] [1] 1 [444, 514, 2113] 336 C2 x C2 x C84