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 170 Igusa CM invariants of non-normal (D4) fields: 34

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [229, 29, 153] [17] 1 [229, 29, 153] 15 C15
2) [137, 1303, 409348] [1] 1 [137, 1303, 409348] 85 C85
3) [109, 541, 17989] [1] 1 [109, 541, 17989] 85 C85
4) [8, 1778, 789673] [1] 1 [8, 1778, 789673] 85 C85
5) [8, 1826, 831769] [1] 1 [8, 1826, 831769] 85 C85
6) [8, 1698, 719833] [1] 1 [8, 1698, 719833] 85 C85
7) [8, 1542, 593641] [1] 1 [8, 1542, 593641] 85 C85
8) [8, 1666, 685177] [1] 1 [8, 1666, 685177] 85 C85
9) [8, 1218, 337081] [1] 1 [8, 1218, 337081] 85 C85
10) [8, 414, 42337] [1] 1 [8, 414, 42337] 85 C85
11) [5, 1217, 367021] [1] 1 [5, 1217, 367021] 85 C85
12) [5, 1577, 620821] [1] 1 [5, 1577, 620821] 85 C85
13) [5, 1461, 479029] [1] 1 [5, 1461, 479029] 85 C85
14) [5, 1566, 581089] [1] 1 [5, 1566, 581089] 85 C85
15) [5, 1734, 743689] [1] 1 [5, 1734, 743689] 85 C85
16) [5, 1257, 393301] [1] 1 [5, 1257, 393301] 85 C85
17) [5, 1437, 480541] [1] 1 [5, 1437, 480541] 85 C85
18) [5, 993, 222361] [1] 1 [5, 993, 222361] 85 C85
19) [29, 1269, 289309] [1] 1 [29, 1269, 289309] 85 C85
20) [29, 990, 77521] [1] 1 [29, 990, 77521] 85 C85
21) [29, 769, 147253] [1] 1 [29, 769, 147253] 85 C85
22) [313, 535, 70852] [1] 1 [313, 535, 70852] 85 C85
23) [89, 1230, 376801] [1] 1 [89, 1230, 376801] 85 C85
24) [53, 862, 63649] [1] 1 [53, 862, 63649] 85 C85
25) [617, 1023, 72676] [1] 1 [617, 1023, 72676] 85 C85
26) [17, 1398, 471193] [1] 1 [17, 1398, 471193] 85 C85
27) [17, 1838, 842113] [1] 1 [17, 1838, 842113] 85 C85
28) [17, 1518, 562753] [1] 1 [17, 1518, 562753] 85 C85
29) [769, 1015, 48196] [1] 1 [769, 1015, 48196] 85 C85
30) [233, 871, 163972] [1] 1 [233, 871, 163972] 85 C85
31) [41, 1174, 320953] [1] 1 [41, 1174, 320953] 85 C85
32) [41, 1790, 795121] [1] 1 [41, 1790, 795121] 85 C85
33) [2213, 833, 168493] [1] 1 [2213, 833, 168493] 255 C255
34) [353, 343, 9556] [1] 1 [353, 343, 9556] 85 C85