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 70 Igusa CM invariants of non-normal (D4) fields: 122

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 293, 4153] [1] 1 [157, 293, 4153] 35 C35
2) [157, 165, 5825] [1] 2 [157, 165, 5825] 70 C70
3) [1361, 567, 63700] [1] 2 [1361, 567, 63700] 70 C70
4) [1361, 951, 13444] [1] 1 [1361, 951, 13444] 35 C35
5) [229, 274, 10525] [1] 1 [229, 274, 10525] 105 C105
6) [1049, 906, 100309] [1] 1 [1049, 906, 100309] 35 C35
7) [109, 150, 3881] [1] 1 [109, 150, 3881] 35 C35
8) [109, 194, 8973] [1] 1 [109, 194, 8973] 35 C35
9) [1381, 245, 14661] [1] 1 [1381, 245, 14661] 35 C35
10) [13, 225, 12497] [1] 1 [13, 225, 12497] 35 C35
11) [13, 593, 52081] [1] 1 [13, 593, 52081] 35 C35
12) [13, 298, 17989] [1] 1 [13, 298, 17989] 35 C35
13) [13, 249, 15497] [1] 1 [13, 249, 15497] 35 C35
14) [13, 157, 3793] [1] 1 [13, 157, 3793] 35 C35
15) [13, 653, 104233] [1] 1 [13, 653, 104233] 35 C35
16) [13, 237, 13649] [1] 1 [13, 237, 13649] 35 C35
17) [13, 313, 13933] [1] 1 [13, 313, 13933] 35 C35
18) [13, 641, 66889] [1] 1 [13, 641, 66889] 35 C35
19) [13, 590, 79537] [1] 1 [13, 590, 79537] 35 C35
20) [977, 750, 124993] [1] 1 [977, 750, 124993] 35 C35
21) [8, 850, 142537] [1] 1 [8, 850, 142537] 35 C35
22) [8, 1410, 472825] [1] 2 [8, 1410, 472825] 70 C70
23) [8, 586, 51001] [1] 2 [8, 586, 51001] 70 C70
24) [8, 522, 48121] [1] 2 [8, 522, 48121] 70 C70
25) [8, 234, 13681] [1] 1 [8, 234, 13681] 35 C35
26) [8, 386, 35449] [1] 1 [8, 386, 35449] 35 C35
27) [8, 902, 184969] [1] 1 [8, 902, 184969] 35 C35
28) [8, 998, 192553] [1] 1 [8, 998, 192553] 35 C35
29) [8, 1090, 288313] [1] 1 [8, 1090, 288313] 35 C35
30) [8, 598, 70969] [1] 1 [8, 598, 70969] 35 C35
31) [8, 510, 35257] [1] 2 [8, 510, 35257] 70 C70
32) [8, 334, 26737] [1] 1 [8, 334, 26737] 35 C35
33) [8, 1206, 263257] [1] 1 [8, 1206, 263257] 35 C35
34) [8, 646, 101737] [1] 1 [8, 646, 101737] 35 C35
35) [5, 228, 10996] [1] 2 [5, 228, 10996] 70 C70
36) [5, 353, 31121] [1] 1 [5, 353, 31121] 35 C35
37) [5, 351, 29269] [1] 2 [5, 351, 29269] 70 C70
38) [5, 761, 132529] [1] 1 [5, 761, 132529] 35 C35
39) [5, 553, 70501] [1] 1 [5, 553, 70501] 35 C35
40) [5, 337, 26681] [1] 1 [5, 337, 26681] 35 C35
41) [5, 622, 92801] [1] 1 [5, 622, 92801] 35 C35
42) [5, 393, 33961] [1] 1 [5, 393, 33961] 35 C35
43) [5, 749, 138349] [1] 1 [5, 749, 138349] 35 C35
44) [5, 318, 24001] [1] 1 [5, 318, 24001] 35 C35
45) [5, 537, 68581] [1] 1 [5, 537, 68581] 35 C35
46) [5, 1129, 312709] [1] 1 [5, 1129, 312709] 35 C35
47) [5, 677, 109621] [1] 1 [5, 677, 109621] 35 C35
48) [5, 493, 56701] [1] 1 [5, 493, 56701] 35 C35
49) [5, 1041, 218389] [1] 1 [5, 1041, 218389] 35 C35
50) [5, 681, 114229] [1] 1 [5, 681, 114229] 35 C35
51) [5, 1161, 293269] [1] 1 [5, 1161, 293269] 35 C35
52) [5, 534, 66169] [1] 1 [5, 534, 66169] 35 C35
53) [5, 319, 22189] [1] 2 [5, 319, 22189] 70 C70
54) [5, 921, 212029] [1] 1 [5, 921, 212029] 35 C35
55) [5, 273, 16921] [1] 1 [5, 273, 16921] 35 C35
56) [5, 874, 189349] [1] 1 [5, 874, 189349] 35 C35
57) [5, 382, 35201] [1] 1 [5, 382, 35201] 35 C35
58) [5, 303, 22501] [1] 2 [5, 303, 22501] 70 C70
59) [5, 966, 232569] [1] 2 [5, 966, 232569] 70 C70
60) [5, 581, 74929] [1] 1 [5, 581, 74929] 35 C35
61) [5, 614, 76249] [1] 1 [5, 614, 76249] 35 C35
62) [5, 562, 64381] [1] 1 [5, 562, 64381] 35 C35
63) [5, 262, 15541] [1] 2 [5, 262, 15541] 70 C70
64) [5, 589, 86629] [1] 1 [5, 589, 86629] 35 C35
65) [5, 398, 39521] [1] 1 [5, 398, 39521] 35 C35
66) [5, 781, 141209] [1] 1 [5, 781, 141209] 35 C35
67) [5, 342, 25321] [1] 1 [5, 342, 25321] 35 C35
68) [5, 597, 87201] [1] 2 [5, 597, 87201] 70 C70
69) [5, 762, 137941] [1] 1 [5, 762, 137941] 35 C35
70) [5, 646, 97849] [1] 1 [5, 646, 97849] 35 C35
71) [5, 601, 90089] [1] 1 [5, 601, 90089] 35 C35
72) [5, 502, 57881] [1] 1 [5, 502, 57881] 35 C35
73) [5, 429, 44809] [1] 1 [5, 429, 44809] 35 C35
74) [5, 1197, 340501] [1] 2 [5, 1197, 340501] 70 C70
75) [5, 829, 158029] [1] 1 [5, 829, 158029] 35 C35
76) [5, 457, 49681] [1] 1 [5, 457, 49681] 35 C35
77) [29, 325, 16481] [1] 1 [29, 325, 16481] 35 C35
78) [29, 525, 48541] [1] 1 [29, 525, 48541] 35 C35
79) [29, 149, 4673] [1] 1 [29, 149, 4673] 35 C35
80) [29, 178, 1396] [1] 2 [29, 178, 1396] 70 C70
81) [1613, 205, 425] [1] 2 [1613, 205, 425] 70 C70
82) [953, 191, 6976] [1] 1 [953, 191, 6976] 35 C35
83) [1549, 237, 4361] [1] 1 [1549, 237, 4361] 35 C35
84) [877, 545, 56497] [1] 1 [877, 545, 56497] 35 C35
85) [428, 222, 1621] [1] 2 [428, 222, 1621] 70 C70
86) [113, 726, 16057] [1] 1 [113, 726, 16057] 35 C35
87) [89, 426, 2293] [1] 1 [89, 426, 2293] 35 C35
88) [53, 330, 21925] [1] 2 [53, 330, 21925] 70 C70
89) [53, 362, 30853] [1] 1 [53, 362, 30853] 35 C35
90) [53, 337, 12161] [1] 1 [53, 337, 12161] 35 C35
91) [53, 357, 28881] [1] 2 [53, 357, 28881] 70 C70
92) [37, 153, 4289] [1] 1 [37, 153, 4289] 35 C35
93) [37, 117, 2969] [1] 1 [37, 117, 2969] 35 C35
94) [37, 845, 176425] [1] 2 [37, 845, 176425] 70 C70
95) [293, 966, 3577] [1] 2 [293, 966, 3577] 70 C70
96) [61, 141, 2393] [1] 1 [61, 141, 2393] 35 C35
97) [61, 225, 12641] [1] 1 [61, 225, 12641] 35 C35
98) [17, 758, 104473] [1] 1 [17, 758, 104473] 35 C35
99) [17, 1175, 338692] [1] 1 [17, 1175, 338692] 35 C35
100) [17, 966, 124489] [1] 1 [17, 966, 124489] 35 C35
101) [17, 1206, 85081] [1] 1 [17, 1206, 85081] 35 C35
102) [17, 1807, 811684] [1] 1 [17, 1807, 811684] 35 C35
103) [17, 1350, 428425] [1] 2 [17, 1350, 428425] 70 C70
104) [17, 178, 7309] [1] 1 [17, 178, 7309] 35 C35
105) [17, 1543, 563044] [1] 1 [17, 1543, 563044] 35 C35
106) [373, 69, 1097] [1] 1 [373, 69, 1097] 35 C35
107) [173, 802, 5101] [1] 1 [173, 802, 5101] 35 C35
108) [773, 1337, 361669] [1] 2 [773, 1337, 361669] 70 C70
109) [181, 161, 6073] [1] 1 [181, 161, 6073] 35 C35
110) [1013, 53, 449] [1] 1 [1013, 53, 449] 35 C35
111) [44, 300, 13876] [1] 2 [44, 300, 13876] 70 C70
112) [44, 238, 4261] [1] 2 [44, 238, 4261] 70 C70
113) [389, 286, 14225] [1] 1 [389, 286, 14225] 35 C35
114) [389, 301, 769] [1] 1 [389, 301, 769] 35 C35
115) [613, 350, 20817] [1] 1 [613, 350, 20817] 35 C35
116) [1097, 975, 7012] [1] 1 [1097, 975, 7012] 35 C35
117) [41, 354, 3613] [1] 1 [41, 354, 3613] 35 C35
118) [41, 1319, 377284] [1] 1 [41, 1319, 377284] 35 C35
119) [41, 582, 19081] [1] 1 [41, 582, 19081] 35 C35
120) [41, 630, 96601] [1] 1 [41, 630, 96601] 35 C35
121) [101, 201, 9873] [1] 2 [101, 201, 9873] 70 C70
122) [1949, 49, 113] [1] 1 [1949, 49, 113] 35 C35