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 18 Igusa CM invariants of non-normal (D4) fields: 170

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [157, 102, 89] [1] 1 [157, 102, 89] 9 C9
2) [809, 103, 832] [1] 1 [809, 103, 832] 9 C9
3) [2689, 63, 320] [1] 1 [2689, 63, 320] 9 C9
4) [10909, 153, 3125] [1] 1 [10909, 153, 3125] 45 C45
5) [137, 143, 4804] [1] 1 [137, 143, 4804] 9 C9
6) [3889, 63, 20] [1] 1 [3889, 63, 20] 27 C3 x C9
7) [109, 153, 5825] [1] 1 [109, 153, 5825] 9 C9
8) [109, 217, 3897] [1] 1 [109, 217, 3897] 9 C9
9) [641, 29, 50] [1] 1 [641, 29, 50] 9 C9
10) [3061, 109, 2205] [1] 1 [3061, 109, 2205] 9 C9
11) [3769, 67, 180] [1] 1 [3769, 67, 180] 9 C9
12) [7489, 87, 20] [1] 1 [7489, 87, 20] 9 C9
13) [821, 169, 2009] [1] 1 [821, 169, 2009] 9 C9
14) [13, 257, 5953] [1] 1 [13, 257, 5953] 9 C9
15) [13, 57, 809] [1] 1 [13, 57, 809] 9 C9
16) [13, 133, 2989] [1] 2 [13, 133, 2989] 18 C18
17) [13, 49, 337] [2, 2] 1 [13, 49, 337] 9 C9
18) [13, 37, 313] [1] 1 [13, 37, 313] 9 C9
19) [13, 149, 5521] [1] 1 [13, 149, 5521] 9 C9
20) [13, 197, 3121] [1] 1 [13, 197, 3121] 9 C9
21) [13, 245, 6553] [1] 1 [13, 245, 6553] 9 C9
22) [13, 49, 337] [1] 1 [13, 49, 337] 9 C9
23) [13, 125, 2473] [1] 1 [13, 125, 2473] 9 C9
24) [1741, 170, 261] [1] 1 [1741, 170, 261] 9 C9
25) [8, 194, 8761] [1] 1 [8, 194, 8761] 9 C9
26) [8, 278, 18169] [1] 1 [8, 278, 18169] 9 C9
27) [8, 122, 2753] [1] 1 [8, 122, 2753] 9 C9
28) [8, 58, 769] [1] 1 [8, 58, 769] 9 C9
29) [8, 330, 18513] [1] 4 [8, 330, 18513] 36 C2 x C18
30) [8, 62, 929] [1] 1 [8, 62, 929] 9 C9
31) [8, 134, 4201] [1] 1 [8, 134, 4201] 9 C9
32) [8, 262, 12553] [1] 1 [8, 262, 12553] 9 C9
33) [8, 194, 9337] [1] 1 [8, 194, 9337] 9 C9
34) [8, 150, 4057] [1] 1 [8, 150, 4057] 9 C9
35) [8, 174, 7281] [1] 2 [8, 174, 7281] 18 C18
36) [8, 198, 8233] [1] 1 [8, 198, 8233] 9 C9
37) [8, 182, 7993] [1] 1 [8, 182, 7993] 9 C9
38) [8, 90, 1993] [1] 2 [8, 90, 1993] 18 C18
39) [8, 130, 4153] [1] 1 [8, 130, 4153] 9 C9
40) [8, 182, 7129] [1] 1 [8, 182, 7129] 9 C9
41) [8, 162, 6361] [1] 1 [8, 162, 6361] 9 C9
42) [8, 154, 4961] [1] 2 [8, 154, 4961] 18 C18
43) [8, 106, 2417] [1] 1 [8, 106, 2417] 9 C9
44) [8, 150, 5113] [1] 1 [8, 150, 5113] 9 C9
45) [8, 58, 641] [1] 1 [8, 58, 641] 9 C9
46) [8, 94, 2081] [1] 1 [8, 94, 2081] 9 C9
47) [8, 258, 16633] [1] 1 [8, 258, 16633] 9 C9
48) [8, 114, 3049] [1] 1 [8, 114, 3049] 9 C9
49) [5, 237, 12681] [1] 2 [5, 237, 12681] 18 C18
50) [5, 246, 14409] [1] 2 [5, 246, 14409] 18 C18
51) [5, 134, 3769] [1] 1 [5, 134, 3769] 9 C9
52) [5, 189, 8269] [1] 1 [5, 189, 8269] 9 C9
53) [5, 206, 10289] [1] 1 [5, 206, 10289] 9 C9
54) [5, 381, 34929] [1] 2 [5, 381, 34929] 18 C18
55) [5, 177, 7281] [1] 2 [5, 177, 7281] 18 C18
56) [5, 109, 2689] [1] 1 [5, 109, 2689] 9 C9
57) [5, 229, 12829] [1] 1 [5, 229, 12829] 9 C9
58) [5, 153, 5701] [1] 1 [5, 153, 5701] 9 C9
59) [5, 126, 3889] [1] 1 [5, 126, 3889] 9 C9
60) [5, 47, 541] [1] 2 [5, 47, 541] 18 C18
61) [5, 209, 10909] [1] 1 [5, 209, 10909] 9 C9
62) [5, 138, 4261] [1] 1 [5, 138, 4261] 9 C9
63) [5, 153, 5821] [1] 1 [5, 153, 5821] 9 C9
64) [5, 174, 7489] [1] 1 [5, 174, 7489] 9 C9
65) [5, 741, 135369] [1] 4 [5, 741, 135369] 36 C2 x C18
66) [5, 201, 10069] [1] 1 [5, 201, 10069] 9 C9
67) [5, 134, 3769] [2, 2] 1 [5, 134, 3769] 9 C9
68) [5, 226, 12589] [1] 1 [5, 226, 12589] 9 C9
69) [5, 174, 7489] [2, 2] 1 [5, 174, 7489] 9 C9
70) [5, 329, 25529] [1] 2 [5, 329, 25529] 18 C18
71) [5, 269, 17989] [1] 1 [5, 269, 17989] 9 C9
72) [5, 93, 1801] [1] 1 [5, 93, 1801] 9 C9
73) [5, 209, 9209] [1] 1 [5, 209, 9209] 9 C9
74) [5, 157, 6101] [1] 1 [5, 157, 6101] 9 C9
75) [5, 249, 15349] [1] 1 [5, 249, 15349] 9 C9
76) [5, 46, 449] [2, 2] 1 [5, 46, 449] 3 C3
77) [5, 117, 3061] [1] 1 [5, 117, 3061] 9 C9
78) [5, 269, 16189] [1] 1 [5, 269, 16189] 9 C9
79) [5, 181, 6829] [1] 1 [5, 181, 6829] 9 C9
80) [5, 166, 6569] [1] 1 [5, 166, 6569] 9 C9
81) [5, 261, 14029] [1] 1 [5, 261, 14029] 9 C9
82) [29, 49, 593] [1] 1 [29, 49, 593] 9 C9
83) [29, 221, 3329] [1] 1 [29, 221, 3329] 9 C9
84) [29, 169, 2609] [1] 1 [29, 169, 2609] 9 C9
85) [29, 190, 1601] [1] 1 [29, 190, 1601] 9 C9
86) [29, 122, 2677] [1] 1 [29, 122, 2677] 9 C9
87) [29, 130, 3181] [1] 1 [29, 130, 3181] 9 C9
88) [29, 85, 1741] [1] 1 [29, 85, 1741] 9 C9
89) [941, 33, 37] [1] 1 [941, 33, 37] 9 C9
90) [5701, 101, 1125] [1] 1 [5701, 101, 1125] 9 C9
91) [1613, 41, 17] [1] 1 [1613, 41, 17] 9 C9
92) [6361, 81, 50] [1] 1 [6361, 81, 50] 9 C9
93) [2753, 61, 242] [1] 1 [2753, 61, 242] 9 C9
94) [757, 37, 153] [1] 1 [757, 37, 153] 9 C9
95) [1973, 101, 2057] [1] 1 [1973, 101, 2057] 9 C9
96) [257, 87, 1828] [1] 1 [257, 87, 1828] 27 C3 x C9
97) [257, 66, 61] [1] 1 [257, 66, 61] 27 C3 x C9
98) [877, 149, 3577] [1] 1 [877, 149, 3577] 9 C9
99) [877, 33, 53] [1] 1 [877, 33, 53] 9 C9
100) [1093, 61, 657] [1] 1 [1093, 61, 657] 45 C45
101) [313, 55, 52] [1] 1 [313, 55, 52] 9 C9
102) [313, 55, 52] [2] 1 [313, 55, 52] 9 C9
103) [149, 110, 641] [1] 1 [149, 110, 641] 9 C9
104) [149, 21, 73] [1] 1 [149, 21, 73] 9 C9
105) [1109, 53, 425] [1] 1 [1109, 53, 425] 9 C9
106) [113, 606, 3217] [1] 1 [113, 606, 3217] 9 C9
107) [113, 119, 1252] [2] 1 [113, 119, 1252] 3 C3
108) [857, 159, 964] [1] 1 [857, 159, 964] 9 C9
109) [10069, 157, 3645] [1] 1 [10069, 157, 3645] 27 C3 x C9
110) [89, 78, 97] [2] 1 [89, 78, 97] 3 C3
111) [53, 129, 2557] [1] 1 [53, 129, 2557] 9 C9
112) [53, 133, 593] [1] 1 [53, 133, 593] 9 C9
113) [53, 66, 877] [1] 1 [53, 66, 877] 9 C9
114) [332, 48, 244] [1] 2 [332, 48, 244] 18 C18
115) [5821, 121, 2205] [1] 1 [5821, 121, 2205] 27 C3 x C9
116) [6569, 83, 80] [1] 1 [6569, 83, 80] 9 C9
117) [1373, 145, 4913] [1] 1 [1373, 145, 4913] 27 C3 x C9
118) [37, 101, 2097] [1] 1 [37, 101, 2097] 9 C9
119) [37, 241, 13401] [1] 1 [37, 241, 13401] 9 C9
120) [61, 190, 5121] [1] 1 [61, 190, 5121] 9 C9
121) [61, 33, 257] [1] 1 [61, 33, 257] 9 C9
122) [197, 57, 369] [1] 2 [197, 57, 369] 18 C18
123) [593, 98, 29] [1] 1 [593, 98, 29] 9 C9
124) [17, 103, 2308] [2, 2] 1 [17, 103, 2308] 3 C3
125) [17, 303, 22948] [1] 1 [17, 303, 22948] 9 C9
126) [17, 167, 6628] [2] 1 [17, 167, 6628] 3 C3
127) [17, 74, 757] [1] 1 [17, 74, 757] 9 C9
128) [17, 334, 5857] [1] 1 [17, 334, 5857] 9 C9
129) [17, 319, 24484] [1] 1 [17, 319, 24484] 9 C9
130) [17, 351, 29572] [1] 1 [17, 351, 29572] 9 C9
131) [17, 174, 7297] [1] 1 [17, 174, 7297] 9 C9
132) [17, 106, 1109] [1] 1 [17, 106, 1109] 9 C9
133) [17, 111, 3076] [2] 1 [17, 111, 3076] 3 C3
134) [17, 222, 5521] [1] 1 [17, 222, 5521] 9 C9
135) [17, 78, 1249] [2, 2] 1 [17, 78, 1249] 3 C3
136) [17, 98, 701] [1] 1 [17, 98, 701] 9 C9
137) [17, 262, 7369] [1] 1 [17, 262, 7369] 9 C9
138) [17, 198, 8713] [1] 1 [17, 198, 8713] 9 C9
139) [173, 105, 637] [1] 2 [173, 105, 637] 18 C18
140) [2081, 47, 32] [1] 1 [2081, 47, 32] 45 C45
141) [3049, 57, 50] [1] 1 [3049, 57, 50] 9 C9
142) [701, 49, 425] [1] 1 [701, 49, 425] 9 C9
143) [2473, 139, 4212] [1] 1 [2473, 139, 4212] 9 C9
144) [653, 33, 109] [1] 1 [653, 33, 109] 9 C9
145) [44, 144, 4084] [1] 2 [44, 144, 4084] 18 C18
146) [337, 47, 468] [1] 1 [337, 47, 468] 9 C9
147) [10289, 103, 80] [1] 1 [10289, 103, 80] 9 C9
148) [12, 22, 109] [3, 3] 2 [12, 22, 109] 6 C6
149) [769, 29, 18] [1] 1 [769, 29, 18] 9 C9
150) [277, 21, 41] [1] 1 [277, 21, 41] 9 C9
151) [2417, 53, 98] [1] 1 [2417, 53, 98] 9 C9
152) [1181, 97, 2057] [1] 1 [1181, 97, 2057] 9 C9
153) [73, 42, 149] [1] 1 [73, 42, 149] 9 C9
154) [233, 87, 436] [2] 1 [233, 87, 436] 9 C9
155) [233, 95, 1732] [1] 1 [233, 95, 1732] 9 C9
156) [233, 51, 592] [1] 1 [233, 51, 592] 9 C9
157) [233, 87, 436] [1] 1 [233, 87, 436] 9 C9
158) [3121, 103, 1872] [1] 1 [3121, 103, 1872] 45 C45
159) [7993, 91, 72] [1] 1 [7993, 91, 72] 9 C9
160) [41, 126, 3313] [1] 1 [41, 126, 3313] 9 C9
161) [41, 111, 1348] [2] 1 [41, 111, 1348] 3 C3
162) [41, 135, 3316] [2] 1 [41, 135, 3316] 9 C9
163) [41, 135, 3316] [1] 1 [41, 135, 3316] 9 C9
164) [41, 42, 277] [1] 1 [41, 42, 277] 9 C9
165) [1801, 91, 1620] [1] 1 [1801, 91, 1620] 9 C9
166) [829, 149, 369] [1] 1 [829, 149, 369] 9 C9
167) [9209, 203, 8000] [1] 1 [9209, 203, 8000] 9 C9
168) [353, 39, 292] [2] 1 [353, 39, 292] 3 C3
169) [929, 31, 8] [1] 1 [929, 31, 8] 9 C9
170) [101, 113, 137] [1] 1 [101, 113, 137] 9 C9