Cremona's table of elliptic curves

83490 = 2 · 3 · 5 · 11² · 23

Class	r	Atkin-Lehner	Eigenvalues
83490a (1 curve)	1	2+ 3+ 5+ 11+ 23+	2+ 3+ 5+ -2 11+  2  3  0
Curve Equation t Generators 83490a1 [1,1,0,15002,-14889662] 1 [44643564:1993431133:21952]
83490b (2 curves)	1	2+ 3+ 5+ 11+ 23+	2+ 3+ 5+ -2 11+  2 -4  0
Curve Equation t Generators 83490b1 [1,1,0,-92411068,341881227472] 2 [288766456:-23380794620:24389] 83490b2 [1,1,0,-88806588,369780623568] 2 [-142233864:20321116932:24389]
83490c (4 curves)	2	2+ 3+ 5+ 11- 23+	2+ 3+ 5+  0 11-  2 -6 -4
Curve Equation t Generators 83490c1 [1,1,0,-41263,1439893] 2 [-214:833:1]&[-93:2164:1] 83490c2 [1,1,0,-334083,-73463463] 4 [-348:1071:1]&[-334:1167:1] 83490c3 [1,1,0,-27953,-202589097] 2 [983:26360:1]&[13534:535555:8] 83490c4 [1,1,0,-5325333,-4732296213] 2 [-10658:5343:8]&[3779:168781:1]
83490d (4 curves)	0	2+ 3+ 5+ 11- 23+	2+ 3+ 5+  0 11- -6 -2  0
Curve Equation t 83490d1 [1,1,0,-543413,273714093] 2 83490d2 [1,1,0,-10455733,13003115437] 4 83490d3 [1,1,0,-12236853,8268542253] 2 83490d4 [1,1,0,-167271733,832617621037] 2
83490e (1 curve)	0	2+ 3+ 5+ 11- 23+	2+ 3+ 5+  3 11- -3  4 -6
Curve Equation t 83490e1 [1,1,0,45252,27702] 1
83490f (4 curves)	1	2+ 3+ 5+ 11- 23-	2+ 3+ 5+  0 11- -2 -6 -4
Curve Equation t Generators 83490f1 [1,1,0,1087,2117493] 2 [18:1455:1] 83490f2 [1,1,0,-240913,44564293] 4 [-82:8027:1] 83490f3 [1,1,0,-519213,-78054687] 2 [1011:20271:1] 83490f4 [1,1,0,-3834613,2888618473] 2 [-324:64171:1]
83490g (2 curves)	1	2+ 3+ 5+ 11- 23-	2+ 3+ 5+  2 11-  6  4  0
Curve Equation t Generators 83490g1 [1,1,0,482,-36428] 2 [31:82:1] 83490g2 [1,1,0,-14038,-620132] 2 [999:30863:1]
83490h (6 curves)	1	2+ 3+ 5- 11- 23+	2+ 3+ 5-  0 11-  2  6 -4
Curve Equation t Generators 83490h1 [1,1,0,-12397057,231846496501] 2 [-6453:211039:1] 83490h2 [1,1,0,-646785537,6283024451829] 4 [-27967:1594546:1] 83490h3 [1,1,0,-1117001217,-4062002637579] 2 [-206592757:-10203445809:6859] 83490h4 [1,1,0,-10326785537,403916128451829] 4 [-2609610:604525621:27] 83490h5 [1,1,0,-10305005537,405704749967829] 2 [-17894120865:4147185816814:185193] 83490h6 [1,1,0,-165228565537,25850839762935829] 2 [37819515:-43072405754:27]
83490i (1 curve)	1	2+ 3+ 5- 11- 23+	2+ 3+ 5- -1 11- -3 -5 -3
Curve Equation t Generators 83490i1 [1,1,0,-30252,56016] 1 [-133:1389:1]
83490j (1 curve)	1	2+ 3+ 5- 11- 23+	2+ 3+ 5-  2 11-  4  3  2
Curve Equation t Generators 83490j1 [1,1,0,-12707,555141] 1 [-5:789:1]
83490k (1 curve)	1	2+ 3+ 5- 11- 23+	2+ 3+ 5-  3 11- -1  3  7
Curve Equation t Generators 83490k1 [1,1,0,-523932,-145998486] 1 [-407:376:1]
83490l (1 curve)	1	2+ 3+ 5- 11- 23+	2+ 3+ 5-  3 11- -4  0  5
Curve Equation t Generators 83490l1 [1,1,0,-78652,-8601776] 1 [325:382:1]
83490m (1 curve)	1	2+ 3+ 5- 11- 23+	2+ 3+ 5- -4 11- -2  6 -7
Curve Equation t Generators 83490m1 [1,1,0,-5934839462,-177318516005484] 1 [119724766635844840456771399578016028490490975424506229311203079982350839016926263208592902103329484002949749321884102542300:105389547188355552280328382010531458333046697253553863570819128779000253870266001941853196630903860774195224733786247368547858:152786435505263623080781455600882489618858808835217595333247106042920200400063255519299586231116469144937076347535177]
83490n (6 curves)	0	2+ 3+ 5- 11- 23-	2+ 3+ 5-  0 11-  2 -2  4
Curve Equation t 83490n1 [1,1,0,494888,7921984] 2 83490n2 [1,1,0,-1983192,60952896] 4 83490n3 [1,1,0,-21149592,-37309693824] 2 83490n4 [1,1,0,-22466072,40875139584] 4 83490n5 [1,1,0,-13449152,74008713816] 2 83490n6 [1,1,0,-359209072,2620259170984] 2
83490o (1 curve)	0	2+ 3+ 5- 11- 23-	2+ 3+ 5- -1 11- -3  3 -3
Curve Equation t 83490o1 [1,1,0,-22550772,41208919536] 1
83490p (1 curve)	0	2+ 3+ 5- 11- 23-	2+ 3+ 5-  3 11-  3 -2  4
Curve Equation t 83490p1 [1,1,0,-76258437,-256373407539] 1
83490q (1 curve)	0	2+ 3+ 5- 11- 23-	2+ 3+ 5-  3 11-  7 -1 -1
Curve Equation t 83490q1 [1,1,0,-370867,83730541] 1
83490r (2 curves)	2	2+ 3+ 5- 11- 23-	2+ 3+ 5- -4 11- -4 -8  2
Curve Equation t Generators 83490r1 [1,1,0,-6052,-93056] 2 [-60:272:1]&[84:-32:1] 83490r2 [1,1,0,20568,-662724] 2 [105:-1686:1]&[62:894:1]
83490s (2 curves)	2	2+ 3- 5+ 11+ 23+	2+ 3- 5+ -2 11+  2 -4 -8
Curve Equation t Generators 83490s1 [1,0,1,-179,-178] 2 [-12:22:1]&[24:85:1] 83490s2 [1,0,1,701,-1234] 2 [3:28:1]&[19:-148:1]
83490t (2 curves)	1	2+ 3- 5+ 11- 23+	2+ 3- 5+  1 11-  4  6 -2
Curve Equation t Generators 83490t1 [1,0,1,-509,10712] 1 [3:-98:1] 83490t2 [1,0,1,-55949,5089016] 1 [135:-38:1]
83490u (1 curve)	1	2+ 3- 5+ 11- 23+	2+ 3- 5+ -1 11-  4  2 -6
Curve Equation t Generators 83490u1 [1,0,1,-124754,192549476] 1 [1341:48697:1]
83490v (2 curves)	0	2+ 3- 5+ 11- 23-	2+ 3- 5+  0 11-  0 -6 -4
Curve Equation t 83490v1 [1,0,1,16211,820136] 2 83490v2 [1,0,1,-95109,7811032] 2
83490w (2 curves)	1	2+ 3- 5- 11+ 23+	2+ 3- 5-  0 11+ -2 -2 -4
Curve Equation t Generators 83490w1 [1,0,1,-553,65756] 2 [55:-478:1] 83490w2 [1,0,1,-28053,1792756] 2 [65:-528:1]
83490x (1 curve)	1	2+ 3- 5- 11+ 23+	2+ 3- 5-  1 11+  0 -2  7
Curve Equation t Generators 83490x1 [1,0,1,-9848,-379744] 1 [120:352:1]
83490y (2 curves)	0	2+ 3- 5- 11+ 23-	2+ 3- 5- -2 11+  4  2 -6
Curve Equation t 83490y1 [1,0,1,-180452870843,-29504891943978442] 2 83490y2 [1,0,1,-180452844223,-29504901084210994] 2
83490z (1 curve)	0	2+ 3- 5- 11+ 23-	2+ 3- 5- -2 11+ -6  7  4
Curve Equation t 83490z1 [1,0,1,-409588,110509298] 1
83490ba (1 curve)	0	2+ 3- 5- 11+ 23-	2+ 3- 5-  5 11+  4  2  1
Curve Equation t 83490ba1 [1,0,1,107,2528] 1
83490bb (6 curves)	0	2+ 3- 5- 11- 23+	2+ 3- 5-  0 11-  2  6 -4
Curve Equation t 83490bb1 [1,0,1,-50823,-4842422] 2 83490bb2 [1,0,1,-834903,-293697494] 4 83490bb3 [1,0,1,-856683,-277571582] 4 83490bb4 [1,0,1,-13358403,-18793411694] 2 83490bb5 [1,0,1,1063587,-1344473594] 2 83490bb6 [1,0,1,-3125433,1821475918] 2
83490bc (2 curves)	0	2+ 3- 5- 11- 23+	2+ 3- 5-  0 11- -4  4 -2
Curve Equation t 83490bc1 [1,0,1,-20514738698,277702342967036] 2 83490bc2 [1,0,1,79259576822,2185945991876348] 2
83490bd (2 curves)	0	2+ 3- 5- 11- 23+	2+ 3- 5-  0 11- -4 -6  8
Curve Equation t 83490bd1 [1,0,1,-29648,1970846] 2 83490bd2 [1,0,1,-474928,125936798] 2
83490be (1 curve)	0	2+ 3- 5- 11- 23+	2+ 3- 5-  3 11- -1 -5  1
Curve Equation t 83490be1 [1,0,1,-70018,-7082242] 1
83490bf (1 curve)	1	2+ 3- 5- 11- 23-	2+ 3- 5-  1 11- -1  8  2
Curve Equation t Generators 83490bf1 [1,0,1,-77443,-10980994] 1 [670:15092:1]
83490bg (1 curve)	1	2+ 3- 5- 11- 23-	2+ 3- 5-  3 11-  5 -2  4
Curve Equation t Generators 83490bg1 [1,0,1,403532,1390999058] 1 [1264:61985:1]
83490bh (1 curve)	1	2+ 3- 5- 11- 23-	2+ 3- 5- -5 11- -1 -1 -7
Curve Equation t Generators 83490bh1 [1,0,1,-278,1736] 1 [2:33:1]
83490bi (1 curve)	0	2- 3+ 5+ 11+ 23+	2- 3+ 5+  2 11+ -2 -3  0
Curve Equation t 83490bi1 [1,1,1,124,11243] 1
83490bj (2 curves)	0	2- 3+ 5+ 11+ 23+	2- 3+ 5+  2 11+ -2  4  0
Curve Equation t 83490bj1 [1,1,1,-11181739291,-455099822461591] 2 83490bj2 [1,1,1,-10745597211,-492231737954967] 2
83490bk (2 curves)	1	2- 3+ 5+ 11- 23+	2- 3+ 5+  2 11-  2  0  4
Curve Equation t Generators 83490bk1 [1,1,1,20749,2723249] 2 [99:-2450:1] 83490bk2 [1,1,1,-211571,32738993] 2 [-511:3038:1]
83490bl (1 curve)	1	2- 3+ 5+ 11- 23+	2- 3+ 5+ -2 11-  0 -1  6
Curve Equation t Generators 83490bl1 [1,1,1,11069,-5332447] 1 [259:-4002:1]
83490bm (1 curve)	0	2- 3+ 5+ 11- 23-	2- 3+ 5+  1 11-  5 -2  0
Curve Equation t 83490bm1 [1,1,1,9582774,3935694423] 1
83490bn (2 curves)	0	2- 3+ 5+ 11- 23-	2- 3+ 5+ -4 11-  0 -2  0
Curve Equation t 83490bn1 [1,1,1,20144,562673] 2 83490bn2 [1,1,1,-91176,4659249] 2
83490bo (1 curve)	0	2- 3+ 5- 11- 23+	2- 3+ 5-  1 11-  3 -4  6
Curve Equation t 83490bo1 [1,1,1,-170328980,855549038675] 1
83490bp (1 curve)	0	2- 3+ 5- 11- 23+	2- 3+ 5-  1 11-  3  5  3
Curve Equation t 83490bp1 [1,1,1,-3660555,-92859975] 1
83490bq (1 curve)	0	2- 3+ 5- 11- 23+	2- 3+ 5-  1 11- -4 -4 -1
Curve Equation t 83490bq1 [1,1,1,-203985735,-1122414559683] 1
83490br (2 curves)	0	2- 3+ 5- 11- 23+	2- 3+ 5-  2 11-  2  0 -8
Curve Equation t 83490br1 [1,1,1,-2756080,120910310225] 2 83490br2 [1,1,1,-383818960,2857856339537] 2
83490bs (1 curve)	0	2- 3+ 5- 11- 23+	2- 3+ 5- -3 11-  1 -3 -7
Curve Equation t 83490bs1 [1,1,1,-63395835,194007005787] 1
83490bt (1 curve)	0	2- 3+ 5- 11- 23+	2- 3+ 5- -3 11-  7  0  2
Curve Equation t 83490bt1 [1,1,1,-1114110,-453453285] 1
83490bu (1 curve)	0	2- 3+ 5- 11- 23+	2- 3+ 5-  4 11-  2 -6  7
Curve Equation t 83490bu1 [1,1,1,-49048260,133199730885] 1
83490bv (4 curves)	0	2- 3+ 5- 11- 23+	2- 3+ 5- -4 11- -2  6 -4
Curve Equation t 83490bv1 [1,1,1,-193905,-17308785] 4 83490bv2 [1,1,1,-2671985,-1681587313] 4 83490bv3 [1,1,1,-2246065,-2235112945] 2 83490bv4 [1,1,1,-42747185,-107592325873] 2
83490bw (2 curves)	0	2- 3+ 5- 11- 23+	2- 3+ 5- -4 11- -4  6  4
Curve Equation t 83490bw1 [1,1,1,-1515,40437] 2 83490bw2 [1,1,1,-29345,1921745] 2
83490bx (2 curves)	1	2- 3+ 5- 11- 23-	2- 3+ 5-  0 11- -4  4 -2
Curve Equation t Generators 83490bx1 [1,1,1,-515160,-140985063] 2 [-423:1421:1] 83490bx2 [1,1,1,-89240,-366552295] 2 [1073:27293:1]
83490by (1 curve)	1	2- 3+ 5- 11- 23-	2- 3+ 5-  1 11-  3 -3  3
Curve Equation t Generators 83490by1 [1,1,1,-186370,-31045585] 1 [-15980:7981:64]
83490bz (1 curve)	1	2- 3+ 5- 11- 23-	2- 3+ 5- -3 11- -7  1  1
Curve Equation t Generators 83490bz1 [1,1,1,-44874970,-111669724825] 1 [-4055:62379:1]
83490ca (4 curves)	1	2- 3+ 5- 11- 23-	2- 3+ 5-  4 11- -6 -6  0
Curve Equation t Generators 83490ca1 [1,1,1,-89122855,323803789277] 4 [1887:401986:1] 83490ca2 [1,1,1,-89277735,322621683165] 4 [-3917:784418:1] 83490ca3 [1,1,1,-32949815,724780500797] 2 [26857:4369796:1] 83490ca4 [1,1,1,-148083735,-155188828035] 2 [-5127:687618:1]
83490cb (2 curves)	1	2- 3- 5+ 11+ 23+	2- 3- 5+  2 11+ -2  4  8
Curve Equation t Generators 83490cb1 [1,0,0,-21601,214985] 2 [266:3515:1] 83490cb2 [1,0,0,84879,1727001] 2 [66:2727:1]
83490cc (1 curve)	0	2- 3- 5+ 11- 23+	2- 3- 5+  1 11- -4 -2  6
Curve Equation t 83490cc1 [1,0,0,-1031,-144759] 1
83490cd (2 curves)	0	2- 3- 5+ 11- 23+	2- 3- 5+ -1 11- -4 -6  2
Curve Equation t 83490cd1 [1,0,0,-61531,-14319535] 3 83490cd2 [1,0,0,-6769771,-6780250399] 1
83490ce (1 curve)	0	2- 3- 5+ 11- 23+	2- 3- 5+ -2 11- -4 -5 -6
Curve Equation t 83490ce1 [1,0,0,-4661,-186009] 1
83490cf (4 curves)	0	2- 3- 5+ 11- 23+	2- 3- 5+  4 11-  4  0 -2
Curve Equation t 83490cf1 [1,0,0,-4847081,-3558646695] 2 83490cf2 [1,0,0,8036999,-19248879319] 2 83490cf3 [1,0,0,-101697296,394299269376] 2 83490cf4 [1,0,0,-74438416,610456736000] 2
83490cg (2 curves)	0	2- 3- 5+ 11- 23+	2- 3- 5+ -5 11-  4  0  1
Curve Equation t 83490cg1 [1,0,0,-40356,-3908574] 1 83490cg2 [1,0,0,302679,35677665] 1
83490ch (4 curves)	1	2- 3- 5+ 11- 23-	2- 3- 5+  0 11-  6  6 -4
Curve Equation t Generators 83490ch1 [1,0,0,-73026,7558596] 2 [-12:2910:1] 83490ch2 [1,0,0,-111746,-1339260] 4 [-254:3394:1] 83490ch3 [1,0,0,444854,-10578820] 2 [206:9374:1] 83490ch4 [1,0,0,-1287866,-561407604] 2 [-650:1414:1]
83490ci (2 curves)	1	2- 3- 5+ 11- 23-	2- 3- 5+ -2 11-  4 -3 -2
Curve Equation t Generators 83490ci1 [1,0,0,-10592766,-13277370204] 1 [6654:455868:1] 83490ci2 [1,0,0,9152619,-54761873055] 1 [6170:483335:1]
83490cj (2 curves)	0	2- 3- 5- 11+ 23+	2- 3- 5-  0 11+  2  2  4
Curve Equation t 83490cj1 [1,0,0,-66855,-87588423] 2 83490cj2 [1,0,0,-3394355,-2389552923] 2
83490ck (1 curve)	0	2- 3- 5- 11+ 23+	2- 3- 5- -1 11+  0  2 -7
Curve Equation t 83490ck1 [1,0,0,-1191550,504247382] 1
83490cl (2 curves)	1	2- 3- 5- 11+ 23-	2- 3- 5-  2 11+ -4 -2  6
Curve Equation t Generators 83490cl1 [1,0,0,-1491346040,22167326439600] 2 [1426900:-702065:64] 83490cl2 [1,0,0,-1491345820,22167333306812] 2 [18284:996878:1]
83490cm (1 curve)	1	2- 3- 5- 11+ 23-	2- 3- 5-  2 11+  6 -7 -4
Curve Equation t Generators 83490cm1 [1,0,0,-3385,-83335] 1 [142:1447:1]
83490cn (1 curve)	1	2- 3- 5- 11+ 23-	2- 3- 5- -5 11+ -4 -2 -1
Curve Equation t Generators 83490cn1 [1,0,0,13005,-3352095] 1 [252:-4119:1]
83490co (2 curves)	1	2- 3- 5- 11- 23+	2- 3- 5-  1 11-  1  0 -2
Curve Equation t Generators 83490co1 [1,0,0,4535,-1867183] 1 [164:1733:1] 83490co2 [1,0,0,-40840,50595392] 1 [-56:7288:1]
83490cp (2 curves)	1	2- 3- 5- 11- 23+	2- 3- 5- -2 11-  4 -3 -2
Curve Equation t Generators 83490cp1 [1,0,0,-6649255,8506751177] 1 [824:-60307:1] 83490cp2 [1,0,0,-580742830,5386665493892] 1 [13892:-11302:1]
83490cq (1 curve)	1	2- 3- 5- 11- 23+	2- 3- 5- -3 11-  1  5 -1
Curve Equation t Generators 83490cq1 [1,0,0,-8472120,9417991650] 1 [-306390:29597335:216]
83490cr (4 curves)	0	2- 3- 5- 11- 23-	2- 3- 5-  0 11-  2 -2  0
Curve Equation t 83490cr1 [1,0,0,-1515,-12495] 2 83490cr2 [1,0,0,-11195,446337] 4 83490cr3 [1,0,0,905,1363517] 2 83490cr4 [1,0,0,-178175,28933125] 2
83490cs (1 curve)	0	2- 3- 5- 11- 23-	2- 3- 5-  5 11-  1  1  7
Curve Equation t 83490cs1 [1,0,0,-33580,-2344528] 1

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations