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 180 Igusa CM invariants of non-normal (D4) fields: 142

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [236, 74, 838] [1] 1 [236, 74, 838] 90 C90
2) [137, 846, 176737] [1] 1 [137, 846, 176737] 90 C90
3) [137, 1022, 83569] [1] 1 [137, 1022, 83569] 90 C90
4) [88, 210, 10937] [1] 1 [88, 210, 10937] 90 C90
5) [88, 358, 28873] [1] 1 [88, 358, 28873] 90 C90
6) [88, 886, 41017] [1] 1 [88, 886, 41017] 90 C90
7) [1137, 715, 2452] [1] 1 [1137, 715, 2452] 90 C90
8) [104, 272, 10072] [1] 1 [104, 272, 10072] 180 C180
9) [104, 626, 74569] [1] 1 [104, 626, 74569] 180 C180
10) [1049, 1055, 87076] [1] 1 [1049, 1055, 87076] 90 C90
11) [97, 49, 382] [1] 1 [97, 49, 382] 90 C90
12) [57, 1543, 558148] [1] 1 [57, 1543, 558148] 90 C90
13) [13, 93, 2081] [5, 5] 1 [13, 93, 2081] 15 C15
14) [8, 686, 117137] [1] 1 [8, 686, 117137] 90 C90
15) [8, 1878, 881593] [1] 1 [8, 1878, 881593] 90 C90
16) [8, 1686, 706777] [1] 1 [8, 1686, 706777] 90 C90
17) [8, 1682, 691081] [1] 1 [8, 1682, 691081] 90 C90
18) [8, 698, 61249] [1] 1 [8, 698, 61249] 90 C90
19) [8, 638, 55553] [1] 1 [8, 638, 55553] 90 C90
20) [8, 1250, 378457] [1] 1 [8, 1250, 378457] 90 C90
21) [8, 1294, 243377] [1] 1 [8, 1294, 243377] 90 C90
22) [8, 1878, 880921] [1] 1 [8, 1878, 880921] 90 C90
23) [8, 426, 43057] [1] 1 [8, 426, 43057] 90 C90
24) [8, 224, 12526] [1] 1 [8, 224, 12526] 90 C3 x C30
25) [8, 1542, 572809] [1] 1 [8, 1542, 572809] 90 C90
26) [8, 1298, 333001] [1] 1 [8, 1298, 333001] 90 C90
27) [8, 1410, 430777] [1] 1 [8, 1410, 430777] 90 C90
28) [8, 1618, 653833] [1] 1 [8, 1618, 653833] 90 C90
29) [5, 1361, 429049] [1] 1 [5, 1361, 429049] 90 C90
30) [5, 1769, 744929] [1] 1 [5, 1769, 744929] 90 C90
31) [5, 214, 11369] [4, 4] 1 [5, 214, 11369] 15 C15
32) [5, 1737, 745261] [1] 1 [5, 1737, 745261] 90 C90
33) [5, 1797, 804301] [1] 1 [5, 1797, 804301] 90 C90
34) [5, 1454, 528449] [1] 1 [5, 1454, 528449] 90 C90
35) [5, 1377, 449881] [1] 1 [5, 1377, 449881] 90 C90
36) [5, 1941, 899089] [1] 1 [5, 1941, 899089] 90 C90
37) [5, 1429, 503849] [1] 1 [5, 1429, 503849] 90 C90
38) [5, 1457, 527201] [1] 1 [5, 1457, 527201] 90 C90
39) [5, 1446, 468649] [1] 1 [5, 1446, 468649] 90 C90
40) [5, 1541, 550889] [1] 1 [5, 1541, 550889] 90 C90
41) [5, 1941, 941869] [1] 1 [5, 1941, 941869] 90 C3 x C30
42) [5, 1177, 313121] [1] 1 [5, 1177, 313121] 90 C90
43) [5, 1357, 459161] [1] 1 [5, 1357, 459161] 90 C90
44) [5, 49, 569] [5, 25] 1 [5, 49, 569] 3 C3
45) [5, 1198, 329921] [1] 1 [5, 1198, 329921] 90 C90
46) [5, 1781, 706529] [1] 1 [5, 1781, 706529] 90 C90
47) [5, 969, 227329] [1] 1 [5, 969, 227329] 90 C90
48) [5, 2126, 1001969] [1] 1 [5, 2126, 1001969] 90 C90
49) [5, 1201, 351569] [1] 1 [5, 1201, 351569] 90 C90
50) [5, 1254, 391849] [1] 1 [5, 1254, 391849] 90 C90
51) [5, 1409, 436369] [1] 1 [5, 1409, 436369] 90 C90
52) [5, 158, 5521] [6, 6] 1 [5, 158, 5521] 15 C15
53) [29, 1385, 471661] [1] 1 [29, 1385, 471661] 90 C90
54) [29, 417, 21541] [1] 1 [29, 417, 21541] 90 C90
55) [29, 1469, 498709] [1] 1 [29, 1469, 498709] 90 C90
56) [29, 166, 5033] [2, 2] 1 [29, 166, 5033] 30 C30
57) [92, 930, 171697] [1] 1 [92, 930, 171697] 90 C90
58) [92, 762, 108361] [1] 1 [92, 762, 108361] 90 C90
59) [905, 1071, 96484] [1] 1 [905, 1071, 96484] 360 C360
60) [849, 538, 41797] [1] 1 [849, 538, 41797] 90 C90
61) [93, 697, 65629] [1] 1 [93, 697, 65629] 90 C90
62) [24, 146, 5113] [3, 3] 1 [24, 146, 5113] 30 C30
63) [24, 130, 2281] [3, 3] 1 [24, 130, 2281] 30 C30
64) [24, 226, 12553] [1] 1 [24, 226, 12553] 90 C90
65) [257, 1271, 333892] [1] 1 [257, 1271, 333892] 270 C3 x C90
66) [428, 66, 982] [1] 1 [428, 66, 982] 90 C90
67) [2249, 735, 40036] [1] 1 [2249, 735, 40036] 360 C360
68) [40, 234, 13649] [1] 1 [40, 234, 13649] 180 C2 x C90
69) [149, 293, 10697] [1] 1 [149, 293, 10697] 90 C3 x C30
70) [908, 978, 6673] [1] 1 [908, 978, 6673] 90 C3 x C30
71) [509, 1689, 713053] [1] 1 [509, 1689, 713053] 90 C90
72) [113, 1623, 643588] [1] 1 [113, 1623, 643588] 90 C90
73) [248, 730, 23857] [1] 1 [248, 730, 23857] 90 C3 x C30
74) [89, 429, 45454] [1] 1 [89, 429, 45454] 90 C90
75) [89, 1679, 694948] [1] 1 [89, 1679, 694948] 90 C90
76) [89, 599, 31828] [1] 1 [89, 599, 31828] 90 C90
77) [533, 750, 4177] [1] 1 [533, 750, 4177] 180 C2 x C90
78) [689, 534, 27193] [1] 1 [689, 534, 27193] 360 C360
79) [53, 1021, 97357] [1] 1 [53, 1021, 97357] 90 C90
80) [53, 278, 5753] [2, 2] 1 [53, 278, 5753] 30 C30
81) [53, 341, 25241] [1] 1 [53, 341, 25241] 90 C3 x C30
82) [53, 617, 60709] [1] 1 [53, 617, 60709] 90 C90
83) [61, 213, 10961] [1] 1 [61, 213, 10961] 90 C90
84) [1461, 1213, 367477] [1] 1 [1461, 1213, 367477] 90 C90
85) [965, 981, 8749] [1] 1 [965, 981, 8749] 180 C180
86) [17, 1443, 491284] [1] 1 [17, 1443, 491284] 90 C90
87) [17, 1026, 72157] [1] 1 [17, 1026, 72157] 90 C90
88) [17, 1878, 880633] [1] 1 [17, 1878, 880633] 90 C90
89) [17, 278, 12521] [1] 1 [17, 278, 12521] 90 C90
90) [17, 278, 12521] [2, 2] 1 [17, 278, 12521] 90 C90
91) [17, 118, 3209] [4, 4] 1 [17, 118, 3209] 45 C45
92) [17, 1806, 815137] [1] 1 [17, 1806, 815137] 90 C90
93) [17, 1758, 765841] [1] 1 [17, 1758, 765841] 90 C90
94) [17, 1251, 385432] [1] 1 [17, 1251, 385432] 90 C90
95) [3065, 399, 20644] [1] 1 [3065, 399, 20644] 180 C180
96) [773, 1473, 509773] [1] 1 [773, 1473, 509773] 90 C90
97) [653, 1577, 608509] [1] 1 [653, 1577, 608509] 90 C90
98) [653, 173, 3401] [1] 1 [653, 173, 3401] 90 C90
99) [44, 1266, 330289] [1] 1 [44, 1266, 330289] 90 C90
100) [44, 954, 206233] [1] 1 [44, 954, 206233] 90 C90
101) [44, 1546, 557929] [1] 1 [44, 1546, 557929] 90 C90
102) [1985, 807, 19396] [1] 1 [1985, 807, 19396] 180 C180
103) [1985, 947, 219736] [1] 1 [1985, 947, 219736] 180 C180
104) [12, 1526, 167017] [1] 1 [12, 1526, 167017] 90 C90
105) [12, 622, 34513] [1] 1 [12, 622, 34513] 90 C90
106) [12, 1138, 173233] [1] 1 [12, 1138, 173233] 90 C90
107) [12, 1090, 204097] [1] 1 [12, 1090, 204097] 90 C90
108) [12, 1070, 135697] [1] 1 [12, 1070, 135697] 90 C90
109) [12, 1318, 341353] [1] 1 [12, 1318, 341353] 90 C90
110) [12, 638, 94849] [1] 1 [12, 638, 94849] 90 C90
111) [12, 1078, 288793] [1] 1 [12, 1078, 288793] 90 C90
112) [12, 1154, 176977] [1] 1 [12, 1154, 176977] 90 C90
113) [12, 430, 45457] [1] 1 [12, 430, 45457] 90 C90
114) [21, 1165, 203221] [1] 1 [21, 1165, 203221] 90 C3 x C30
115) [21, 1285, 338461] [1] 1 [21, 1285, 338461] 90 C90
116) [21, 206, 10273] [2, 2] 1 [21, 206, 10273] 30 C30
117) [21, 430, 43201] [1] 1 [21, 430, 43201] 90 C90
118) [21, 1069, 124909] [1] 1 [21, 1069, 124909] 90 C90
119) [85, 601, 35029] [1] 1 [85, 601, 35029] 180 C180
120) [85, 213, 11321] [1] 1 [85, 213, 11321] 180 C2 x C90
121) [233, 285, 10462] [1] 1 [233, 285, 10462] 90 C90
122) [56, 858, 154417] [1] 1 [56, 858, 154417] 90 C90
123) [41, 935, 214036] [1] 1 [41, 935, 214036] 90 C90
124) [41, 83, 1220] [5] 1 [41, 83, 1220] 18 C18
125) [41, 83, 1220] [2, 10] 1 [41, 83, 1220] 18 C18
126) [41, 1566, 596689] [1] 1 [41, 1566, 596689] 90 C90
127) [41, 1839, 843748] [1] 1 [41, 1839, 843748] 90 C90
128) [41, 386, 35773] [1] 1 [41, 386, 35773] 90 C90
129) [365, 837, 6421] [1] 1 [365, 837, 6421] 180 C2 x C90
130) [365, 301, 21829] [1] 1 [365, 301, 21829] 180 C180
131) [101, 449, 49769] [1] 1 [101, 449, 49769] 90 C3 x C30
132) [101, 641, 51589] [1] 1 [101, 641, 51589] 90 C90
133) [101, 13, 17] [25] 1 [101, 13, 17] 3 C3
134) [65, 1767, 775876] [1] 1 [65, 1767, 775876] 180 C180
135) [65, 1091, 264664] [1] 1 [65, 1091, 264664] 180 C180
136) [65, 309, 19174] [1] 1 [65, 309, 19174] 180 C180
137) [65, 118, 2441] [1] 1 [65, 118, 2441] 180 C2 x C90
138) [65, 1182, 223441] [1] 1 [65, 1182, 223441] 180 C2 x C90
139) [65, 1686, 694009] [1] 1 [65, 1686, 694009] 180 C180
140) [65, 354, 31069] [1] 1 [65, 354, 31069] 180 C2 x C90
141) [65, 1367, 449476] [1] 1 [65, 1367, 449476] 180 C180
142) [65, 118, 2441] [2, 2] 1 [65, 118, 2441] 180 C2 x C90