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

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 510, 2225] [1] 2 [157, 510, 2225] 28 C28
2) [237, 233, 241] [1] 1 [237, 233, 241] 14 C14
3) [437, 65, 73] [1] 1 [437, 65, 73] 14 C14
4) [437, 90, 277] [1] 1 [437, 90, 277] 14 C14
5) [236, 40, 164] [1] 1 [236, 40, 164] 14 C14
6) [88, 78, 113] [1] 1 [88, 78, 113] 14 C14
7) [213, 65, 577] [1] 1 [213, 65, 577] 14 C14
8) [213, 345, 6273] [1] 1 [213, 345, 6273] 14 C14
9) [205, 166, 3609] [1] 1 [205, 166, 3609] 28 C28
10) [821, 262, 4025] [1] 1 [821, 262, 4025] 14 C14
11) [13, 590, 40225] [1] 2 [13, 590, 40225] 28 C28
12) [13, 294, 11417] [1] 2 [13, 294, 11417] 28 C28
13) [13, 233, 10033] [1] 1 [13, 233, 10033] 14 C14
14) [13, 473, 52393] [1] 2 [13, 473, 52393] 28 C28
15) [13, 485, 52225] [1] 2 [13, 485, 52225] 28 C28
16) [13, 350, 13777] [1] 1 [13, 350, 13777] 14 C14
17) [13, 257, 11569] [1] 1 [13, 257, 11569] 14 C14
18) [13, 174, 2369] [1] 1 [13, 174, 2369] 14 C14
19) [8, 158, 4193] [1] 1 [8, 158, 4193] 14 C14
20) [8, 56, 622] [1] 1 [8, 56, 622] 14 C14
21) [8, 114, 3217] [1] 1 [8, 114, 3217] 28 C28
22) [8, 222, 11169] [1] 2 [8, 222, 11169] 28 C2 x C14
23) [8, 330, 15057] [1] 2 [8, 330, 15057] 28 C2 x C14
24) [8, 262, 17089] [1] 1 [8, 262, 17089] 28 C2 x C14
25) [8, 142, 4393] [1] 1 [8, 142, 4393] 28 C2 x C14
26) [8, 338, 14449] [1] 1 [8, 338, 14449] 28 C28
27) [8, 122, 2369] [1] 1 [8, 122, 2369] 14 C14
28) [8, 238, 12593] [1] 2 [8, 238, 12593] 28 C2 x C14
29) [8, 234, 13561] [1] 1 [8, 234, 13561] 28 C2 x C14
30) [8, 510, 36225] [1] 4 [8, 510, 36225] 56 C2 x C2 x C14
31) [8, 48, 334] [1] 1 [8, 48, 334] 14 C14
32) [8, 710, 97225] [1] 1 [8, 710, 97225] 28 C28
33) [8, 770, 103225] [1] 2 [8, 770, 103225] 28 C28
34) [8, 72, 1198] [1] 1 [8, 72, 1198] 14 C14
35) [8, 170, 7217] [1] 1 [8, 170, 7217] 14 C14
36) [8, 162, 3361] [1] 2 [8, 162, 3361] 28 C28
37) [8, 94, 2177] [1] 1 [8, 94, 2177] 14 C14
38) [8, 106, 1457] [1] 1 [8, 106, 1457] 14 C14
39) [8, 122, 1921] [1] 1 [8, 122, 1921] 14 C14
40) [8, 342, 25369] [1] 1 [8, 342, 25369] 14 C14
41) [8, 502, 39673] [1] 1 [8, 502, 39673] 14 C14
42) [8, 450, 28153] [1] 1 [8, 450, 28153] 14 C14
43) [8, 120, 2350] [1] 2 [8, 120, 2350] 28 C2 x C14
44) [1957, 45, 17] [1] 1 [1957, 45, 17] 42 C42
45) [5, 381, 34189] [1] 1 [5, 381, 34189] 14 C14
46) [5, 501, 53289] [1] 2 [5, 501, 53289] 28 C2 x C14
47) [5, 202, 10021] [1] 1 [5, 202, 10021] 14 C14
48) [5, 401, 36949] [1] 1 [5, 401, 36949] 14 C14
49) [5, 366, 27009] [1] 2 [5, 366, 27009] 28 C28
50) [5, 246, 13849] [1] 1 [5, 246, 13849] 14 C14
51) [5, 154, 5209] [1] 2 [5, 154, 5209] 28 C28
52) [5, 333, 27441] [1] 2 [5, 333, 27441] 28 C28
53) [5, 549, 61569] [1] 2 [5, 549, 61569] 28 C28
54) [5, 156, 5764] [1] 1 [5, 156, 5764] 28 C2 x C14
55) [5, 681, 103689] [1] 2 [5, 681, 103689] 28 C2 x C14
56) [5, 861, 180369] [1] 4 [5, 861, 180369] 56 C2 x C28
57) [5, 277, 17821] [1] 1 [5, 277, 17821] 14 C14
58) [5, 166, 6169] [1] 1 [5, 166, 6169] 14 C14
59) [5, 741, 131989] [1] 2 [5, 741, 131989] 28 C2 x C14
60) [5, 108, 2596] [1] 2 [5, 108, 2596] 28 C2 x C14
61) [5, 301, 22289] [1] 1 [5, 301, 22289] 14 C14
62) [5, 721, 107849] [1] 2 [5, 721, 107849] 28 C2 x C14
63) [5, 246, 14809] [1] 1 [5, 246, 14809] 14 C14
64) [5, 481, 47029] [1] 1 [5, 481, 47029] 14 C14
65) [5, 289, 18569] [1] 1 [5, 289, 18569] 14 C14
66) [5, 137, 4681] [1] 1 [5, 137, 4681] 14 C14
67) [5, 297, 18801] [1] 2 [5, 297, 18801] 28 C28
68) [5, 298, 20581] [1] 1 [5, 298, 20581] 14 C14
69) [5, 309, 23089] [1] 1 [5, 309, 23089] 14 C14
70) [5, 114, 3169] [1] 1 [5, 114, 3169] 28 C28
71) [5, 249, 13969] [1] 1 [5, 249, 13969] 14 C14
72) [5, 274, 17149] [1] 1 [5, 274, 17149] 14 C14
73) [5, 189, 7729] [1] 1 [5, 189, 7729] 14 C14
74) [5, 861, 167629] [1] 2 [5, 861, 167629] 28 C2 x C14
75) [5, 111, 3049] [1] 1 [5, 111, 3049] 28 C28
76) [5, 269, 15089] [1] 1 [5, 269, 15089] 14 C14
77) [29, 78, 1057] [1] 1 [29, 78, 1057] 14 C14
78) [29, 301, 13769] [1] 2 [29, 301, 13769] 28 C2 x C14
79) [29, 550, 19481] [1] 2 [29, 550, 19481] 28 C2 x C14
80) [29, 105, 2169] [1] 2 [29, 105, 2169] 28 C28
81) [29, 289, 3473] [1] 1 [29, 289, 3473] 14 C14
82) [29, 249, 4473] [1] 2 [29, 249, 4473] 28 C2 x C14
83) [1256, 142, 17] [1] 1 [1256, 142, 17] 28 C2 x C14
84) [93, 365, 4825] [1] 2 [93, 365, 4825] 28 C2 x C14
85) [24, 76, 1348] [1] 1 [24, 76, 1348] 14 C14
86) [1781, 129, 153] [1] 2 [1781, 129, 153] 56 C2 x C2 x C14
87) [141, 69, 873] [1] 1 [141, 69, 873] 14 C14
88) [152, 62, 353] [1] 1 [152, 62, 353] 14 C14
89) [152, 116, 932] [1] 1 [152, 116, 932] 14 C14
90) [40, 254, 3169] [1] 1 [40, 254, 3169] 28 C2 x C14
91) [149, 102, 217] [1] 1 [149, 102, 217] 14 C14
92) [149, 65, 721] [1] 1 [149, 65, 721] 14 C14
93) [53, 190, 1393] [1] 1 [53, 190, 1393] 14 C14
94) [53, 205, 2225] [1] 2 [53, 205, 2225] 28 C28
95) [53, 366, 2961] [1] 2 [53, 366, 2961] 28 C2 x C14
96) [53, 385, 20825] [1] 4 [53, 385, 20825] 56 C2 x C2 x C14
97) [1052, 208, 1348] [1] 1 [1052, 208, 1348] 14 C14
98) [37, 545, 22225] [1] 2 [37, 545, 22225] 28 C2 x C14
99) [37, 326, 5257] [1] 1 [37, 326, 5257] 14 C14
100) [293, 414, 657] [1] 2 [293, 414, 657] 28 C28
101) [28, 64, 772] [1] 1 [28, 64, 772] 14 C14
102) [445, 581, 35329] [1] 1 [445, 581, 35329] 56 C56
103) [33, 43, 388] [1] 1 [33, 43, 388] 14 C14
104) [197, 342, 873] [1] 2 [197, 342, 873] 28 C28
105) [1461, 293, 21097] [1] 1 [1461, 293, 21097] 14 C14
106) [1304, 294, 16393] [1] 1 [1304, 294, 16393] 42 C42
107) [232, 196, 8676] [1] 1 [232, 196, 8676] 28 C2 x C14
108) [133, 153, 233] [1] 1 [133, 153, 233] 14 C14
109) [77, 281, 1241] [1] 1 [77, 281, 1241] 14 C14
110) [77, 61, 449] [1] 1 [77, 61, 449] 14 C14
111) [77, 69, 1017] [1] 2 [77, 69, 1017] 28 C2 x C14
112) [653, 393, 30613] [1] 1 [653, 393, 30613] 14 C14
113) [44, 72, 1252] [1] 1 [44, 72, 1252] 14 C14
114) [44, 120, 3204] [1] 2 [44, 120, 3204] 28 C2 x C14
115) [12, 142, 4609] [1] 1 [12, 142, 4609] 14 C14
116) [12, 122, 1993] [1] 1 [12, 122, 1993] 14 C14
117) [12, 70, 550] [1] 2 [12, 70, 550] 28 C2 x C14
118) [12, 350, 11425] [1] 2 [12, 350, 11425] 28 C2 x C14
119) [12, 218, 4969] [1] 1 [12, 218, 4969] 14 C14
120) [12, 178, 5893] [1] 2 [12, 178, 5893] 28 C2 x C14
121) [12, 34, 214] [1] 1 [12, 34, 214] 14 C14
122) [12, 100, 1177] [1] 2 [12, 100, 1177] 28 C2 x C14
123) [12, 158, 4513] [1] 1 [12, 158, 4513] 14 C14
124) [12, 214, 3949] [1] 2 [12, 214, 3949] 28 C2 x C14
125) [12, 178, 6193] [1] 1 [12, 178, 6193] 14 C14
126) [12, 76, 1417] [1] 2 [12, 76, 1417] 28 C2 x C14
127) [12, 58, 649] [1] 1 [12, 58, 649] 14 C14
128) [12, 112, 949] [1] 2 [12, 112, 949] 28 C2 x C14
129) [21, 85, 1549] [1] 1 [21, 85, 1549] 14 C14
130) [21, 85, 1801] [1] 1 [21, 85, 1801] 14 C14
131) [21, 281, 4993] [1] 1 [21, 281, 4993] 14 C14
132) [21, 61, 673] [1] 1 [21, 61, 673] 14 C14
133) [21, 125, 1129] [1] 1 [21, 125, 1129] 14 C14
134) [21, 73, 697] [1] 1 [21, 73, 697] 14 C14
135) [85, 221, 11169] [1] 1 [85, 221, 11169] 28 C28
136) [85, 289, 17289] [1] 1 [85, 289, 17289] 28 C28
137) [56, 876, 51844] [1] 1 [56, 876, 51844] 14 C14
138) [485, 209, 7889] [1] 1 [485, 209, 7889] 28 C28
139) [353, 311, 4324] [1] 1 [353, 311, 4324] 14 C14
140) [101, 361, 1649] [1] 1 [101, 361, 1649] 14 C14