Cremona's table of elliptic curves

88218 = 2 · 3² · 13² · 29

Class	r	Atkin-Lehner	Eigenvalues
88218a (2 curves)	1	2+ 3+ 13+ 29+	2+ 3+  0  1 -3 13+  3 -2
Curve Equation t Generators 88218a1 [1,-1,0,-597,5877] 1 [-6:99:1] 88218a2 [1,-1,0,2523,24389] 1 [46:463:1]
88218b (1 curve)	1	2+ 3+ 13+ 29+	2+ 3+  0 -3 -1 13+  7  0
Curve Equation t Generators 88218b1 [1,-1,0,-12,144] 1 [0:12:1]
88218c (1 curve)	1	2+ 3+ 13+ 29+	2+ 3+  1  1  0 13+  1 -1
Curve Equation t Generators 88218c1 [1,-1,0,-59604,-7944624] 1 [3426555:62178609:6859]
88218d (2 curves)	1	2+ 3+ 13+ 29+	2+ 3+  2 -4  0 13+  2  0
Curve Equation t Generators 88218d1 [1,-1,0,-3112251,-2118836251] 2 [8556335461645:249578591191353:3449795831] 88218d2 [1,-1,0,-49837371,-135406913563] 2 [55754785252306218829488689:-8156759553588949068632048307:2361373599108465990307]
88218e (2 curves)	1	2+ 3+ 13+ 29+	2+ 3+ -3  1  0 13+ -3 -5
Curve Equation t Generators 88218e1 [1,-1,0,-24621,1493181] 1 [75:216:1] 88218e2 [1,-1,0,-9411,3296411] 1 [361:6664:1]
88218f (1 curve)	1	2+ 3+ 13+ 29+	2+ 3+  4 -5  3 13+  7  2
Curve Equation t Generators 88218f1 [1,-1,0,5955,-156987] 1 [474:10203:1]
88218g (2 curves)	0	2+ 3+ 13+ 29-	2+ 3+  0  0  4 13+  2 -6
Curve Equation t 88218g1 [1,-1,0,-155427,25043669] 2 88218g2 [1,-1,0,-2528187,1547881037] 2
88218h (2 curves)	0	2+ 3+ 13+ 29-	2+ 3+  0 -1 -3 13+ -3  2
Curve Equation t 88218h1 [1,-1,0,47373,-2047707] 3 88218h2 [1,-1,0,-908322,-339535468] 1
88218i (1 curve)	0	2+ 3+ 13+ 29-	2+ 3+  0  3 -1 13+ -7  0
Curve Equation t 88218i1 [1,-1,0,-18537,-8357491] 1
88218j (1 curve)	0	2+ 3+ 13+ 29-	2+ 3+  3  5 -4 13+  1  5
Curve Equation t 88218j1 [1,-1,0,222,16628] 1
88218k (1 curve)	0	2+ 3+ 13+ 29-	2+ 3+  4  5  3 13+ -7 -2
Curve Equation t 88218k1 [1,-1,0,9057270,9221738228] 1
88218l (1 curve)	0	2+ 3- 13+ 29+	2+ 3-  0  0  3 13+  5  6
Curve Equation t 88218l1 [1,-1,0,-792,-135810] 1
88218m (2 curves)	0	2+ 3- 13+ 29+	2+ 3-  0  0 -4 13+ -2  6
Curve Equation t 88218m1 [1,-1,0,-1709703657,28185223133133] 2 88218m2 [1,-1,0,-27626570217,1767419487614925] 2
88218n (2 curves)	0	2+ 3- 13+ 29+	2+ 3-  0  1  3 13+ -3 -2
Curve Equation t 88218n1 [1,-1,0,-62468262,194696731620] 1 88218n2 [1,-1,0,-5094202437,139947893132373] 1
88218o (1 curve)	0	2+ 3- 13+ 29+	2+ 3-  0  3 -5 13+  1  0
Curve Equation t 88218o1 [1,-1,0,7033833,33251234589] 1
88218p (1 curve)	0	2+ 3- 13+ 29+	2+ 3-  1  1 -6 13+  7  2
Curve Equation t 88218p1 [1,-1,0,-16362189,-25482715803] 1
88218q (1 curve)	0	2+ 3- 13+ 29+	2+ 3-  2 -1 -3 13+  3  0
Curve Equation t 88218q1 [1,-1,0,-44901,44458389] 1
88218r (2 curves)	2	2+ 3- 13+ 29+	2+ 3- -2 -2  0 13+ -2 -4
Curve Equation t Generators 88218r1 [1,-1,0,-9918,311364] 2 [-81:801:1]&[270:819:8] 88218r2 [1,-1,0,20502,1826280] 2 [-68:372:1]&[-29:1113:1]
88218s (4 curves)	2	2+ 3- 13+ 29+	2+ 3- -2 -4 -4 13+ -2 -4
Curve Equation t Generators 88218s1 [1,-1,0,-3044313,83627181] 2 [-705:43701:1]&[-237:28257:1] 88218s2 [1,-1,0,-34194393,76768894125] 4 [-159:286788:1]&[25350:107385:8] 88218s3 [1,-1,0,-20079513,140666955885] 2 [673:356676:1]&[-5918:231447:1] 88218s4 [1,-1,0,-546710553,4920354115821] 2 [12474:-210033:1]&[13530:-681:1]
88218t (1 curve)	0	2+ 3- 13+ 29+	2+ 3-  3  3  6 13+ -7 -5
Curve Equation t 88218t1 [1,-1,0,-85968,10018048] 1
88218u (1 curve)	0	2+ 3- 13+ 29+	2+ 3- -3  3  2 13+ -5 -3
Curve Equation t 88218u1 [1,-1,0,38754,-17172] 1
88218v (1 curve)	0	2+ 3- 13+ 29+	2+ 3- -4 -1  3 13+ -3  0
Curve Equation t 88218v1 [1,-1,0,-3129489,-2130176151] 1
88218w (1 curve)	0	2+ 3- 13+ 29+	2+ 3- -4 -4 -1 13+  7  2
Curve Equation t 88218w1 [1,-1,0,8871201,77164402459] 1
88218x (1 curve)	1	2+ 3- 13+ 29-	2+ 3-  0 -1 -5 13+ -1  6
Curve Equation t Generators 88218x1 [1,-1,0,4759938,560918164] 1 [14492:1757114:1]
88218y (2 curves)	1	2+ 3- 13+ 29-	2+ 3-  0  4  3 13+  3 -2
Curve Equation t Generators 88218y1 [1,-1,0,128493,-11611755] 1 [3707598:43675815:39304] 88218y2 [1,-1,0,-1354482,789016788] 1 [-10866:93651:8]
88218z (1 curve)	1	2+ 3- 13+ 29-	2+ 3- -1 -1  2 13+ -5 -1
Curve Equation t Generators 88218z1 [1,-1,0,-263925,457223989] 1 [-445:22277:1]
88218ba (4 curves)	1	2+ 3- 13+ 29-	2+ 3-  2  0 -4 13+  2 -4
Curve Equation t Generators 88218ba1 [1,-1,0,729,106029] 2 [10:-343:1] 88218ba2 [1,-1,0,-29691,1912977] 4 [-111:2013:1] 88218ba3 [1,-1,0,-75321,-5342193] 2 [829:21978:1] 88218ba4 [1,-1,0,-470781,124447779] 2 [903:20406:1]
88218bb (1 curve)	1	2+ 3- 13+ 29-	2+ 3-  2  1  1 13+ -7  0
Curve Equation t Generators 88218bb1 [1,-1,0,729,-4055] 1 [20:125:1]
88218bc (2 curves)	1	2+ 3- 13+ 29-	2+ 3-  3  1  0 13+ -3 -8
Curve Equation t Generators 88218bc1 [1,-1,0,-572688,-166758318] 1 [1622798081478:62335049603527:868250664] 88218bc2 [1,-1,0,514827,-695587203] 1 [129326:16392895:8]
88218bd (1 curve)	1	2+ 3- 13+ 29-	2+ 3- -3  2 -1 13+  4  8
Curve Equation t Generators 88218bd1 [1,-1,0,-1806,-42184] 1 [830:23454:1]
88218be (2 curves)	1	2+ 3- 13+ 29-	2+ 3- -3 -5  6 13+ -3  1
Curve Equation t Generators 88218be1 [1,-1,0,-11718576,-72789449472] 1 [3871271298594:145228291794561:676836152] 88218be2 [1,-1,0,104706369,1887271069581] 1 [334830:71200947:8]
88218bf (2 curves)	1	2+ 3- 13+ 29-	2+ 3- -4  4  4 13+  2 -6
Curve Equation t Generators 88218bf1 [1,-1,0,-102699,-13799291] 2 [209930:-4338349:343] 88218bf2 [1,-1,0,-1684539,-841101611] 2 [2450:97433:1]
88218bg (2 curves)	1	2+ 3- 13- 29+	2+ 3-  2  2  0 13-  6 -2
Curve Equation t Generators 88218bg1 [1,-1,0,3654,-177228] 2 [1089:35433:1] 88218bg2 [1,-1,0,-33786,-2041740] 2 [-132:390:1]
88218bh (2 curves)	0	2+ 3- 13- 29-	2+ 3-  0  2  0 13-  6  8
Curve Equation t 88218bh1 [1,-1,0,-117402,10367540] 2 88218bh2 [1,-1,0,-1699242,852855524] 2
88218bi (2 curves)	0	2- 3+ 13+ 29+	2- 3+  0  0 -4 13+ -2 -6
Curve Equation t 88218bi1 [1,-1,1,-17270,-921787] 2 88218bi2 [1,-1,1,-280910,-57235291] 2
88218bj (2 curves)	0	2- 3+ 13+ 29+	2- 3+  0 -1  3 13+  3  2
Curve Equation t 88218bj1 [1,-1,1,-100925,12609029] 3 88218bj2 [1,-1,1,426355,54861733] 1
88218bk (1 curve)	0	2- 3+ 13+ 29+	2- 3+  0  3  1 13+  7  0
Curve Equation t 88218bk1 [1,-1,1,-2060,310223] 1
88218bl (1 curve)	0	2- 3+ 13+ 29+	2- 3+ -3  5  4 13+ -1  5
Curve Equation t 88218bl1 [1,-1,1,1996,-450953] 1
88218bm (1 curve)	0	2- 3+ 13+ 29+	2- 3+ -4  5 -3 13+  7 -2
Curve Equation t 88218bm1 [1,-1,1,1006363,-341881315] 1
88218bn (2 curves)	1	2- 3+ 13+ 29-	2- 3+  0  1  3 13+ -3 -2
Curve Equation t Generators 88218bn1 [1,-1,1,280,-997] 1 [39:241:1] 88218bn2 [1,-1,1,-5375,-153305] 1 [91:278:1]
88218bo (1 curve)	1	2- 3+ 13+ 29-	2- 3+  0 -3  1 13+ -7  0
Curve Equation t Generators 88218bo1 [1,-1,1,-110,-3779] 1 [19:17:1]
88218bp (1 curve)	1	2- 3+ 13+ 29-	2- 3+ -1  1  0 13+ -1 -1
Curve Equation t Generators 88218bp1 [1,-1,1,-536438,215041285] 1 [-575:18539:1]
88218bq (2 curves)	1	2- 3+ 13+ 29-	2- 3+ -2 -4  0 13+ -2  0
Curve Equation t Generators 88218bq1 [1,-1,1,-345806,78590685] 2 [153:-5485:1] 88218bq2 [1,-1,1,-5537486,5016916701] 2 [1337:723:1]
88218br (2 curves)	1	2- 3+ 13+ 29-	2- 3+  3  1  0 13+  3 -5
Curve Equation t Generators 88218br1 [1,-1,1,-1046,-121741] 1 [48072:372689:512] 88218br2 [1,-1,1,-221591,-40094297] 1 [31144904:7665640039:512]
88218bs (1 curve)	1	2- 3+ 13+ 29-	2- 3+ -4 -5 -3 13+ -7  2
Curve Equation t Generators 88218bs1 [1,-1,1,53593,4185055] 1 [91:-3178:1]
88218bt (2 curves)	1	2- 3- 13+ 29+	2- 3-  0 -1 -3 13+ -3  2
Curve Equation t Generators 88218bt1 [1,-1,1,-369635,88704659] 1 [-3:9478:1] 88218bt2 [1,-1,1,-30143210,63706497833] 3 [3129:2431:1]
88218bu (1 curve)	1	2- 3- 13+ 29+	2- 3-  0 -3  5 13+  1  0
Curve Equation t Generators 88218bu1 [1,-1,1,41620,15125231] 1 [-171:1813:1]
88218bv (1 curve)	1	2- 3- 13+ 29+	2- 3-  1  3  2 13+  1 -5
Curve Equation t Generators 88218bv1 [1,-1,1,-1262462,-651897957] 1 [769414703351392096:79541034721471991049:70506419683328]
88218bw (2 curves)	1	2- 3- 13+ 29+	2- 3- -1 -1 -2 13+  3  1
Curve Equation t Generators 88218bw1 [1,-1,1,-1553,-8131327] 1 [309:4408:1] 88218bw2 [1,-1,1,-9903263,12032986853] 1 [1905782010:36387169931:1331000]
88218bx (6 curves)	1	2- 3- 13+ 29+	2- 3- -2  0 -4 13+ -2  4
Curve Equation t Generators 88218bx1 [1,-1,1,336109,47068467] 2 [-81:4434:1] 88218bx2 [1,-1,1,-1610771,410745651] 4 [-913:33918:1] 88218bx3 [1,-1,1,-12196931,-16107898413] 2 [-1957:17214:1] 88218bx4 [1,-1,1,-22174691,40181366931] 4 [-1803376:915499755:4096] 88218bx5 [1,-1,1,-18615551,53508210747] 2 [7738110:-614409771:1000] 88218bx6 [1,-1,1,-354756551,2571927517995] 2 [-14090:14298357:8]
88218by (1 curve)	1	2- 3- 13+ 29+	2- 3- -2  1  3 13+  3  0
Curve Equation t Generators 88218by1 [1,-1,1,-266,20297] 1 [-15:151:1]
88218bz (1 curve)	1	2- 3- 13+ 29+	2- 3- -2  2 -1 13+  7  2
Curve Equation t Generators 88218bz1 [1,-1,1,-424391,-121394113] 1 [3195:174838:1]
88218ca (1 curve)	1	2- 3- 13+ 29+	2- 3- -3  3 -4 13+  1  0
Curve Equation t Generators 88218ca1 [1,-1,1,65371,2035037] 1 [205:-5004:1]
88218cb (1 curve)	1	2- 3- 13+ 29+	2- 3-  4  1 -3 13+ -3  0
Curve Equation t Generators 88218cb1 [1,-1,1,-18518,-965311] 1 [3105525:26285281:15625]
88218cc (1 curve)	0	2- 3- 13+ 29-	2- 3-  0  1  5 13+ -1 -6
Curve Equation t 88218cc1 [1,-1,1,28165,248811] 1
88218cd (1 curve)	0	2- 3- 13+ 29-	2- 3-  1 -1  6 13+  7  3
Curve Equation t 88218cd1 [1,-1,1,-7637,282507] 1
88218ce (2 curves)	0	2- 3- 13+ 29-	2- 3-  1  2 -3 13+ -8  0
Curve Equation t 88218ce1 [1,-1,1,7573,-423237] 1 88218ce2 [1,-1,1,-692087,223285443] 1
88218cf (1 curve)	0	2- 3- 13+ 29-	2- 3- -2 -1 -1 13+ -7  0
Curve Equation t 88218cf1 [1,-1,1,123169,-8539293] 1
88218cg (1 curve)	0	2- 3- 13+ 29-	2- 3- -2  2  3 13+ -5  6
Curve Equation t 88218cg1 [1,-1,1,-79120931,-270878927133] 1
88218ch (2 curves)	0	2- 3- 13- 29+	2- 3- -2 -2  0 13-  6  2
Curve Equation t 88218ch1 [1,-1,1,617494,-387517399] 2 88218ch2 [1,-1,1,-5709866,-4502832343] 2
88218ci (2 curves)	1	2- 3- 13- 29-	2- 3-  0 -2  0 13-  6 -8
Curve Equation t Generators 88218ci1 [1,-1,1,-695,4879] 2 [7:14:1] 88218ci2 [1,-1,1,-10055,390511] 2 [37:242:1]

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