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 84 Igusa CM invariants of non-normal (D4) fields: 197

Number Igusa invariants Conductor Components Quartic invariants Class number Class group
1) [317, 753, 123921] [1] 1 [317, 753, 123921] 42 C42
2) [661, 181, 8025] [1] 1 [661, 181, 8025] 42 C42
3) [344, 610, 51401] [1] 1 [344, 610, 51401] 42 C42
4) [157, 305, 14425] [1] 1 [157, 305, 14425] 42 C42
5) [237, 106, 1861] [1] 1 [237, 106, 1861] 42 C42
6) [9769, 137, 2250] [1] 1 [9769, 137, 2250] 42 C42
7) [437, 85, 1697] [1] 1 [437, 85, 1697] 42 C42
8) [437, 65, 73] [2, 2] 2 [437, 65, 73] 14 C14
9) [901, 461, 2449] [1] 1 [901, 461, 2449] 168 C168
10) [269, 414, 4113] [1] 2 [269, 414, 4113] 84 C84
11) [137, 175, 6800] [1] 1 [137, 175, 6800] 42 C42
12) [137, 671, 43204] [1] 1 [137, 671, 43204] 42 C42
13) [7529, 402, 10285] [1] 1 [7529, 402, 10285] 42 C42
14) [88, 530, 50425] [1] 2 [88, 530, 50425] 84 C2 x C42
15) [104, 162, 6457] [1] 1 [104, 162, 6457] 84 C84
16) [104, 372, 34180] [1] 1 [104, 372, 34180] 84 C84
17) [145, 139, 4504] [1] 1 [145, 139, 4504] 168 C168
18) [145, 122, 3141] [1] 1 [145, 122, 3141] 168 C168
19) [109, 685, 40761] [1] 1 [109, 685, 40761] 42 C42
20) [109, 262, 1465] [1] 1 [109, 262, 1465] 42 C42
21) [2381, 658, 22525] [1] 1 [2381, 658, 22525] 42 C42
22) [1765, 137, 721] [1] 1 [1765, 137, 721] 252 C3 x C84
23) [7489, 200, 2511] [1] 1 [7489, 200, 2511] 42 C42
24) [685, 501, 929] [1] 1 [685, 501, 929] 84 C2 x C42
25) [253, 446, 13297] [1] 1 [253, 446, 13297] 42 C42
26) [209, 827, 170512] [1] 1 [209, 827, 170512] 42 C42
27) [209, 216, 1423] [1] 1 [209, 216, 1423] 42 C42
28) [209, 111, 3028] [2] 1 [209, 111, 3028] 42 C42
29) [209, 111, 3028] [1] 1 [209, 111, 3028] 42 C42
30) [1709, 165, 2961] [1] 2 [1709, 165, 2961] 84 C2 x C42
31) [493, 513, 593] [1] 1 [493, 513, 593] 84 C2 x C42
32) [13, 665, 97657] [1] 1 [13, 665, 97657] 42 C42
33) [13, 705, 122225] [1] 2 [13, 705, 122225] 84 C84
34) [13, 549, 24569] [1] 1 [13, 549, 24569] 42 C42
35) [13, 758, 136153] [1] 1 [13, 758, 136153] 42 C42
36) [13, 701, 121417] [1] 1 [13, 701, 121417] 42 C42
37) [13, 157, 6133] [3, 3] 1 [13, 157, 6133] 21 C21
38) [13, 870, 184025] [1] 2 [13, 870, 184025] 84 C2 x C42
39) [13, 298, 21733] [1] 1 [13, 298, 21733] 42 C42
40) [13, 758, 126793] [1] 1 [13, 758, 126793] 42 C42
41) [13, 49, 571] [1] 1 [13, 49, 571] 42 C42
42) [13, 710, 118537] [1] 1 [13, 710, 118537] 42 C42
43) [13, 693, 116081] [1] 2 [13, 693, 116081] 84 C2 x C42
44) [13, 64, 556] [1] 1 [13, 64, 556] 42 C42
45) [76, 366, 3089] [1] 1 [76, 366, 3089] 42 C42
46) [3497, 498, 48013] [1] 1 [3497, 498, 48013] 84 C84
47) [1285, 341, 3049] [1] 1 [1285, 341, 3049] 84 C2 x C42
48) [8, 1026, 134137] [1] 1 [8, 1026, 134137] 42 C42
49) [8, 458, 29969] [1] 1 [8, 458, 29969] 42 C42
50) [8, 658, 108169] [1] 1 [8, 658, 108169] 42 C42
51) [8, 650, 93457] [1] 2 [8, 650, 93457] 84 C2 x C42
52) [8, 1638, 584233] [1] 2 [8, 1638, 584233] 84 C84
53) [8, 2790, 1318825] [1] 2 [8, 2790, 1318825] 84 C2 x C42
54) [8, 430, 36977] [1] 1 [8, 430, 36977] 42 C42
55) [8, 1030, 251113] [1] 1 [8, 1030, 251113] 42 C42
56) [8, 602, 58849] [1] 2 [8, 602, 58849] 84 C2 x C42
57) [8, 234, 10801] [1] 1 [8, 234, 10801] 42 C42
58) [8, 490, 35825] [1] 1 [8, 490, 35825] 42 C42
59) [5, 809, 161089] [1] 1 [5, 809, 161089] 42 C42
60) [5, 405, 34345] [1] 1 [5, 405, 34345] 42 C42
61) [5, 886, 192329] [1] 1 [5, 886, 192329] 42 C42
62) [5, 1701, 620389] [1] 2 [5, 1701, 620389] 84 C2 x C42
63) [5, 661, 90929] [1] 1 [5, 661, 90929] 42 C42
64) [5, 789, 141849] [1] 1 [5, 789, 141849] 42 C42
65) [5, 598, 75881] [1] 1 [5, 598, 75881] 42 C42
66) [5, 533, 66061] [1] 1 [5, 533, 66061] 42 C42
67) [5, 633, 85321] [1] 1 [5, 633, 85321] 42 C42
68) [5, 473, 47321] [1] 1 [5, 473, 47321] 42 C42
69) [5, 709, 124889] [1] 1 [5, 709, 124889] 42 C42
70) [5, 897, 200601] [1] 2 [5, 897, 200601] 84 C2 x C42
71) [5, 766, 144689] [1] 1 [5, 766, 144689] 42 C42
72) [5, 901, 199169] [1] 1 [5, 901, 199169] 42 C42
73) [5, 949, 224369] [1] 1 [5, 949, 224369] 42 C42
74) [5, 697, 104921] [1] 1 [5, 697, 104921] 42 C42
75) [5, 969, 232429] [1] 1 [5, 969, 232429] 42 C42
76) [5, 601, 89249] [1] 1 [5, 601, 89249] 42 C42
77) [5, 929, 203509] [1] 1 [5, 929, 203509] 42 C42
78) [5, 393, 38161] [1] 1 [5, 393, 38161] 42 C42
79) [5, 461, 52849] [1] 1 [5, 461, 52849] 42 C42
80) [5, 433, 46321] [1] 1 [5, 433, 46321] 42 C42
81) [5, 422, 42521] [1] 1 [5, 422, 42521] 42 C42
82) [5, 501, 58689] [1] 1 [5, 501, 58689] 42 C42
83) [5, 689, 111649] [1] 1 [5, 689, 111649] 42 C42
84) [5, 1301, 369589] [1] 1 [5, 1301, 369589] 42 C42
85) [5, 741, 123489] [1] 1 [5, 741, 123489] 42 C42
86) [5, 886, 194969] [1] 1 [5, 886, 194969] 42 C42
87) [5, 726, 128889] [1] 1 [5, 726, 128889] 42 C42
88) [5, 814, 163649] [1] 1 [5, 814, 163649] 42 C42
89) [5, 1573, 617221] [1] 2 [5, 1573, 617221] 84 C2 x C42
90) [5, 942, 221121] [1] 2 [5, 942, 221121] 84 C2 x C42
91) [5, 1017, 258561] [1] 2 [5, 1017, 258561] 84 C84
92) [29, 309, 20673] [1] 1 [29, 309, 20673] 42 C42
93) [29, 574, 59633] [1] 2 [29, 574, 59633] 84 C2 x C42
94) [29, 470, 38521] [1] 1 [29, 470, 38521] 42 C42
95) [29, 610, 41869] [1] 1 [29, 610, 41869] 42 C42
96) [124, 400, 29956] [1] 1 [124, 400, 29956] 42 C42
97) [93, 157, 5581] [1] 1 [93, 157, 5581] 42 C42
98) [93, 278, 17833] [1] 1 [93, 278, 17833] 42 C42
99) [24, 254, 14593] [1] 1 [24, 254, 14593] 42 C42
100) [24, 770, 145321] [1] 2 [24, 770, 145321] 84 C2 x C42
101) [24, 434, 45913] [1] 2 [24, 434, 45913] 84 C2 x C42
102) [24, 340, 22756] [1] 1 [24, 340, 22756] 42 C42
103) [221, 93, 781] [1] 1 [221, 93, 781] 84 C84
104) [413, 190, 2417] [1] 1 [413, 190, 2417] 42 C42
105) [2273, 309, 9664] [1] 1 [2273, 309, 9664] 42 C42
106) [1141, 146, 765] [1] 1 [1141, 146, 765] 42 C42
107) [141, 365, 17761] [1] 1 [141, 365, 17761] 42 C42
108) [141, 689, 115825] [1] 1 [141, 689, 115825] 42 C42
109) [152, 676, 26692] [1] 1 [152, 676, 26692] 42 C42
110) [149, 485, 2149] [1] 1 [149, 485, 2149] 42 C42
111) [149, 101, 2513] [1] 1 [149, 101, 2513] 42 C42
112) [1453, 273, 833] [1] 2 [1453, 273, 833] 84 C2 x C42
113) [3113, 480, 54487] [1] 1 [3113, 480, 54487] 42 C42
114) [1229, 109, 205] [1] 1 [1229, 109, 205] 126 C3 x C42
115) [185, 165, 5650] [1] 1 [185, 165, 5650] 84 C84
116) [89, 519, 40084] [1] 1 [89, 519, 40084] 42 C42
117) [89, 1787, 710032] [1] 1 [89, 1787, 710032] 42 C42
118) [1721, 726, 21625] [1] 1 [1721, 726, 21625] 42 C42
119) [565, 521, 5569] [1] 1 [565, 521, 5569] 84 C2 x C42
120) [497, 390, 6217] [1] 1 [497, 390, 6217] 42 C42
121) [53, 189, 8917] [1] 1 [53, 189, 8917] 42 C42
122) [7681, 277, 1900] [1] 1 [7681, 277, 1900] 42 C42
123) [184, 106, 1153] [1] 1 [184, 106, 1153] 42 C42
124) [37, 521, 49129] [1] 1 [37, 521, 49129] 42 C42
125) [37, 593, 43873] [1] 1 [37, 593, 43873] 42 C42
126) [37, 166, 1561] [2, 2] 1 [37, 166, 1561] 42 C42
127) [37, 461, 43057] [1] 1 [37, 461, 43057] 42 C42
128) [37, 166, 1561] [1] 1 [37, 166, 1561] 42 C42
129) [37, 677, 84529] [1] 1 [37, 677, 84529] 42 C42
130) [37, 481, 57609] [1] 1 [37, 481, 57609] 42 C42
131) [37, 566, 32137] [1] 1 [37, 566, 32137] 42 C42
132) [37, 438, 10073] [1] 1 [37, 438, 10073] 42 C42
133) [37, 833, 169393] [1] 2 [37, 833, 169393] 84 C2 x C42
134) [37, 477, 17801] [1] 1 [37, 477, 17801] 42 C42
135) [37, 350, 25297] [1] 1 [37, 350, 25297] 42 C42
136) [949, 525, 57281] [1] 1 [949, 525, 57281] 84 C84
137) [789, 485, 1801] [1] 1 [789, 485, 1801] 42 C42
138) [7901, 474, 24565] [1] 1 [7901, 474, 24565] 42 C42
139) [61, 605, 51841] [1] 1 [61, 605, 51841] 42 C42
140) [61, 257, 13081] [1] 1 [61, 257, 13081] 42 C42
141) [61, 510, 17201] [1] 1 [61, 510, 17201] 42 C42
142) [61, 29, 73] [13] 1 [61, 29, 73] 3 C3
143) [197, 445, 2177] [1] 1 [197, 445, 2177] 42 C42
144) [17, 530, 20653] [1] 1 [17, 530, 20653] 42 C42
145) [17, 1494, 122809] [1] 1 [17, 1494, 122809] 42 C42
146) [1757, 141, 1017] [1] 2 [1757, 141, 1017] 84 C2 x C42
147) [1037, 421, 497] [1] 1 [1037, 421, 497] 84 C84
148) [173, 233, 3841] [1] 1 [173, 233, 3841] 42 C42
149) [545, 695, 90100] [1] 1 [545, 695, 90100] 84 C84
150) [2801, 474, 44965] [1] 1 [2801, 474, 44965] 42 C42
151) [77, 390, 26937] [1] 2 [77, 390, 26937] 84 C2 x C42
152) [77, 173, 7309] [1] 1 [77, 173, 7309] 42 C42
153) [77, 582, 40329] [1] 2 [77, 582, 40329] 84 C2 x C42
154) [569, 183, 4816] [1] 1 [569, 183, 4816] 42 C42
155) [701, 561, 39249] [1] 1 [701, 561, 39249] 42 C42
156) [389, 113, 2317] [1] 1 [389, 113, 2317] 42 C42
157) [389, 201, 9225] [1] 1 [389, 201, 9225] 42 C42
158) [1157, 45, 217] [1] 1 [1157, 45, 217] 84 C84
159) [1157, 385, 2057] [1] 2 [1157, 385, 2057] 168 C2 x C2 x C42
160) [12, 422, 43321] [1] 1 [12, 422, 43321] 42 C42
161) [12, 590, 67825] [1] 2 [12, 590, 67825] 84 C2 x C42
162) [12, 610, 77473] [1] 1 [12, 610, 77473] 42 C42
163) [12, 106, 1942] [1] 1 [12, 106, 1942] 42 C42
164) [12, 130, 3142] [1] 1 [12, 130, 3142] 42 C42
165) [12, 290, 15217] [1] 1 [12, 290, 15217] 42 C42
166) [12, 458, 24793] [1] 1 [12, 458, 24793] 42 C42
167) [12, 566, 27817] [1] 1 [12, 566, 27817] 42 C42
168) [12, 422, 30649] [1] 1 [12, 422, 30649] 42 C42
169) [21, 590, 70561] [1] 1 [21, 590, 70561] 42 C42
170) [21, 509, 25033] [1] 1 [21, 509, 25033] 42 C42
171) [21, 845, 170521] [1] 2 [21, 845, 170521] 84 C2 x C42
172) [21, 253, 8017] [1] 1 [21, 253, 8017] 42 C42
173) [21, 701, 119569] [1] 1 [21, 701, 119569] 42 C42
174) [21, 166, 6553] [1] 1 [21, 166, 6553] 42 C42
175) [21, 701, 106969] [1] 1 [21, 701, 106969] 42 C42
176) [21, 166, 6553] [2, 2] 1 [21, 166, 6553] 42 C42
177) [21, 289, 14449] [1] 1 [21, 289, 14449] 42 C42
178) [21, 785, 140401] [1] 1 [21, 785, 140401] 42 C42
179) [21, 869, 183073] [1] 2 [21, 869, 183073] 84 C2 x C42
180) [21, 193, 9181] [1] 1 [21, 193, 9181] 42 C42
181) [21, 533, 65977] [1] 1 [21, 533, 65977] 42 C42
182) [21, 85, 1801] [2, 2] 2 [21, 85, 1801] 14 C14
183) [85, 497, 6481] [1] 1 [85, 497, 6481] 84 C2 x C42
184) [601, 599, 35460] [1] 1 [601, 599, 35460] 42 C42
185) [56, 202, 9697] [1] 1 [56, 202, 9697] 42 C42
186) [41, 1415, 496036] [1] 1 [41, 1415, 496036] 42 C42
187) [41, 919, 162340] [1] 1 [41, 919, 162340] 42 C42
188) [201, 103, 1396] [1] 1 [201, 103, 1396] 42 C42
189) [201, 103, 1396] [2] 1 [201, 103, 1396] 42 C42
190) [365, 89, 1889] [1] 1 [365, 89, 1889] 84 C2 x C42
191) [2073, 226, 4477] [1] 1 [2073, 226, 4477] 42 C42
192) [3089, 1502, 119185] [1] 1 [3089, 1502, 119185] 42 C42
193) [101, 534, 13113] [1] 2 [101, 534, 13113] 84 C2 x C42
194) [101, 341, 27025] [1] 1 [101, 341, 27025] 42 C42
195) [481, 254, 8433] [1] 1 [481, 254, 8433] 84 C2 x C42
196) [381, 521, 8329] [1] 1 [381, 521, 8329] 42 C42
197) [69, 533, 14977] [1] 1 [69, 533, 14977] 42 C42