Cremona's table of elliptic curves

67536 = 2⁴ · 3² · 7 · 67

Class	r	Atkin-Lehner	Eigenvalues
67536a (2 curves)	1	2+ 3+ 7+ 67+	2+ 3+  2 7+  0 -2 -4  4
Curve Equation t Generators 67536a1 [0,0,0,-3279,72270] 2 [30:30:1] 67536a2 [0,0,0,-3219,75042] 2 [1:268:1]
67536b (1 curve)	1	2+ 3+ 7+ 67+	2+ 3+  2 7+ -1  1  6  0
Curve Equation t Generators 67536b1 [0,0,0,81,513] 1 [96:945:1]
67536c (2 curves)	1	2+ 3+ 7+ 67+	2+ 3+  2 7+ -6  6  6  0
Curve Equation t Generators 67536c1 [0,0,0,-1977322254,-33842644730725] 2 [1215846822701196346640213785994892556725423851657050973746485412858531629062874654321213006866069200004833295072738260330937765278879790857340818976978154869237969396677731824576416047941467122069197023013:-459768556302442550392355110606074001138816933005187557833395435695609666983115635015661309546240679946017905875194053073882577281010683975141662294984552659554272643751574968502788810240073269605380118215610:7745938273273006904214278899864416565786955080269982283362606098748753790765320006446957570118277095077090122816138825253733493788358026148159243185238533721166136965892751797321510233824819004201631] 67536c2 [0,0,0,-1977254919,-33845064898762] 2 [1557757244744461751825877883316010834136993163518703436415845713083441231507008004562192693086807261179944893:225689307126038057030923594824188390924284454126717142139230243307641531334256879070325381566555858702034678412:25195891184848487554753685190732690215066766189134492683101158774882916726369533043124585074318661649957]
67536d (2 curves)	1	2+ 3+ 7+ 67+	2+ 3+ -2 7+  0 -2  4  4
Curve Equation t Generators 67536d1 [0,0,0,-29511,-1951290] 2 [5439:14248:27] 67536d2 [0,0,0,-28971,-2026134] 2 [441:8424:1]
67536e (1 curve)	1	2+ 3+ 7+ 67+	2+ 3+ -2 7+  1  1 -6  0
Curve Equation t Generators 67536e1 [0,0,0,9,-19] 1 [4:9:1]
67536f (2 curves)	1	2+ 3+ 7+ 67+	2+ 3+ -2 7+  6  6 -6  0
Curve Equation t Generators 67536f1 [0,0,0,-17795900286,913751407729575] 2 [1845292754578271420800454950209044253059321929398788581752206901559:13380042596272863204038863911361598721297073204233107544198806686:23958476934233618153833899575335585502333263427565368674463593] 67536f2 [0,0,0,-17795294271,913816752266574] 2 [427526235857244495425859054089895:3067822451324640261229680271188924:5484733376995544043385847483]
67536g (2 curves)	0	2+ 3- 7+ 67+	2+ 3-  0 7+  0 -4  2  6
Curve Equation t 67536g1 [0,0,0,-107715,13615954] 2 67536g2 [0,0,0,-1723755,871086778] 2
67536h (1 curve)	2	2+ 3- 7+ 67+	2+ 3-  1 7+ -2  1 -6 -6
Curve Equation t Generators 67536h1 [0,0,0,-4107,-101302] 1 [-37:2:1]&[89:488:1]
67536i (1 curve)	0	2+ 3- 7+ 67+	2+ 3- -1 7+  0  3  6  0
Curve Equation t 67536i1 [0,0,0,-678,3971] 1
67536j (1 curve)	0	2+ 3- 7+ 67+	2+ 3- -1 7+  0 -5  2 -8
Curve Equation t 67536j1 [0,0,0,-12078,76491] 1
67536k (1 curve)	0	2+ 3- 7+ 67+	2+ 3-  2 7+  0  4 -1  1
Curve Equation t 67536k1 [0,0,0,36,-1188] 1
67536l (2 curves)	2	2+ 3- 7+ 67+	2+ 3- -2 7+ -2 -2  0  0
Curve Equation t Generators 67536l1 [0,0,0,-1326,18335] 2 [-29:180:1]&[23:2:1] 67536l2 [0,0,0,-111,50654] 2 [-35:108:1]&[25:252:1]
67536m (1 curve)	0	2+ 3- 7+ 67+	2+ 3-  3 7+  0 -1 -4  0
Curve Equation t 67536m1 [0,0,0,-66,-173] 1
67536n (1 curve)	1	2+ 3- 7+ 67-	2+ 3-  0 7+ -3  5  2 -2
Curve Equation t Generators 67536n1 [0,0,0,-75,317] 1 [4:9:1]
67536o (1 curve)	1	2+ 3- 7+ 67-	2+ 3-  1 7+  0  5  6  4
Curve Equation t Generators 67536o1 [0,0,0,-118767,15753278] 1 [-367:3148:1]
67536p (1 curve)	1	2+ 3- 7+ 67-	2+ 3- -2 7+ -3 -3 -6 -4
Curve Equation t Generators 67536p1 [0,0,0,-111,-1811] 1 [20:63:1]
67536q (4 curves)	1	2+ 3- 7+ 67-	2+ 3- -2 7+ -4 -6 -2 -8
Curve Equation t Generators 67536q1 [0,0,0,-12666,-548665] 2 [191:2000:1] 67536q2 [0,0,0,-12711,-544570] 4 [-62:72:1] 67536q3 [0,0,0,-1371,-1481254] 2 [185:2144:1] 67536q4 [0,0,0,-24771,654194] 2 [-101:1458:1]
67536r (2 curves)	1	2+ 3- 7+ 67-	2+ 3- -2 7+  6  2  0  4
Curve Equation t Generators 67536r1 [0,0,0,-1326,-22489] 2 [1394:17955:8] 67536r2 [0,0,0,-22431,-1293010] 2 [206410:1694439:1000]
67536s (1 curve)	1	2+ 3- 7+ 67-	2+ 3-  4 7+  3  1  6  2
Curve Equation t Generators 67536s1 [0,0,0,-17463,924905] 1 [760:20655:1]
67536t (2 curves)	1	2+ 3- 7- 67+	2+ 3-  0 7- -4  4 -2  6
Curve Equation t Generators 67536t1 [0,0,0,225,25758] 2 [-18:126:1] 67536t2 [0,0,0,-11835,481626] 2 [-93:882:1]
67536u (1 curve)	1	2+ 3- 7- 67+	2+ 3-  1 7- -4  5  0  4
Curve Equation t Generators 67536u1 [0,0,0,-11322,-280233] 1 [-29:154:1]
67536v (1 curve)	1	2+ 3- 7- 67+	2+ 3-  3 7-  2 -5 -2 -6
Curve Equation t Generators 67536v1 [0,0,0,-1251,-15822] 1 [-23:28:1]
67536w (1 curve)	1	2+ 3- 7- 67+	2+ 3- -3 7- -4  1 -2  0
Curve Equation t Generators 67536w1 [0,0,0,-32814,2287899] 1 [103:28:1]
67536x (1 curve)	1	2+ 3- 7- 67+	2+ 3- -3 7- -4  1  4  0
Curve Equation t Generators 67536x1 [0,0,0,-86274,-9753669] 1 [-1163123:854:6859]
67536y (1 curve)	0	2+ 3- 7- 67-	2+ 3-  2 7-  5 -5  6  4
Curve Equation t 67536y1 [0,0,0,-2379,-44683] 1
67536z (1 curve)	0	2+ 3- 7- 67-	2+ 3-  3 7- -4 -1  2  4
Curve Equation t 67536z1 [0,0,0,-111,-2] 1
67536ba (2 curves)	0	2- 3+ 7+ 67+	2- 3+  4 7+  2  2  2 -4
Curve Equation t 67536ba1 [0,0,0,-468,-3925] 2 67536ba2 [0,0,0,-7503,-250150] 2
67536bb (2 curves)	2	2- 3+ 7+ 67+	2- 3+ -4 7+ -2  2 -2 -4
Curve Equation t Generators 67536bb1 [0,0,0,-4212,105975] 2 [33:54:1]&[37:28:1] 67536bb2 [0,0,0,-67527,6754050] 2 [-282:1836:1]&[42:1998:1]
67536bc (1 curve)	1	2- 3+ 7+ 67-	2- 3+  2 7+ -1 -1 -2  0
Curve Equation t Generators 67536bc1 [0,0,0,-549,8927] 1 [-26:75:1]
67536bd (2 curves)	1	2- 3+ 7+ 67-	2- 3+  2 7+ -2  0 -6  2
Curve Equation t Generators 67536bd1 [0,0,0,-2484,-33885] 2 [1044263:29189890:1331] 67536bd2 [0,0,0,6561,-223830] 2 [57135561010:-1606239838835:73034632]
67536be (1 curve)	1	2- 3+ 7+ 67-	2- 3+ -2 7+  1 -1  2  0
Curve Equation t Generators 67536be1 [0,0,0,-4941,-241029] 1 [122262:2256687:343]
67536bf (2 curves)	1	2- 3+ 7+ 67-	2- 3+ -2 7+  2  0  6  2
Curve Equation t Generators 67536bf1 [0,0,0,-276,1255] 2 [-14:333:8] 67536bf2 [0,0,0,729,8290] 2 [6054:48655:216]
67536bg (2 curves)	1	2- 3- 7+ 67+	2- 3-  0 7+  0 -2  6  0
Curve Equation t Generators 67536bg1 [0,0,0,240,3971] 2 [37:252:1] 67536bg2 [0,0,0,-2775,50402] 2 [-26:324:1]
67536bh (2 curves)	1	2- 3- 7+ 67+	2- 3-  0 7+ -3 -1 -6 -2
Curve Equation t Generators 67536bh1 [0,0,0,15,-4093] 1 [34:189:1] 67536bh2 [0,0,0,-18885,-998989] 1 [1042:33327:1]
67536bi (1 curve)	1	2- 3- 7+ 67+	2- 3-  1 7+  2 -7  2  2
Curve Equation t Generators 67536bi1 [0,0,0,-507,-2518] 1 [-19:16:1]
67536bj (2 curves)	1	2- 3- 7+ 67+	2- 3-  2 7+  0  0 -2  2
Curve Equation t Generators 67536bj1 [0,0,0,-264,-425] 2 [-14:45:8] 67536bj2 [0,0,0,-3279,-72182] 2 [2066:93870:1]
67536bk (1 curve)	1	2- 3- 7+ 67+	2- 3-  2 7+  0  0 -5 -7
Curve Equation t Generators 67536bk1 [0,0,0,7296,70321372] 1 [674:19530:1]
67536bl (2 curves)	1	2- 3- 7+ 67+	2- 3- -2 7+ -4  2  2  8
Curve Equation t Generators 67536bl1 [0,0,0,-52491,23567546] 2 [-329:2286:1] 67536bl2 [0,0,0,-1596171,773487290] 2 [16823:2176018:1]
67536bm (2 curves)	1	2- 3- 7+ 67+	2- 3- -3 7+  0  5  0 -2
Curve Equation t Generators 67536bm1 [0,0,0,-264,1451] 1 [5:16:1] 67536bm2 [0,0,0,-5304,-148489] 1 [-57101:13232:1331]
67536bn (3 curves)	1	2- 3- 7+ 67+	2- 3- -3 7+ -6  5 -6 -2
Curve Equation t Generators 67536bn1 [0,0,0,-25779,1299314] 1 [425:8192:1] 67536bn2 [0,0,0,-624819,-189978766] 1 [1001:13696:1] 67536bn3 [0,0,0,-50601459,-138545579086] 1 [228091759:28537297184:12167]
67536bo (1 curve)	1	2- 3- 7+ 67+	2- 3-  4 7+  2 -4 -1 -1
Curve Equation t Generators 67536bo1 [0,0,0,6792,-65140] 1 [170:2450:1]
67536bp (1 curve)	0	2- 3- 7+ 67-	2- 3-  0 7+  2 -4  3  5
Curve Equation t 67536bp1 [0,0,0,-9840,4916144] 1
67536bq (2 curves)	0	2- 3- 7+ 67-	2- 3-  0 7+ -4 -4  6  2
Curve Equation t 67536bq1 [0,0,0,-1515,-134566] 2 67536bq2 [0,0,0,-49755,-4254262] 2
67536br (1 curve)	2	2- 3- 7+ 67-	2- 3-  1 7+ -4 -3  0 -4
Curve Equation t Generators 67536br1 [0,0,0,-8067,-192638] 1 [-63:256:1]&[-33:194:1]
67536bs (1 curve)	0	2- 3- 7+ 67-	2- 3- -1 7+ -4 -1  4  6
Curve Equation t 67536bs1 [0,0,0,-48,-61] 1
67536bt (1 curve)	0	2- 3- 7+ 67-	2- 3-  2 7+  0  0 -1  3
Curve Equation t 67536bt1 [0,0,0,-4224,114032] 1
67536bu (4 curves)	0	2- 3- 7+ 67-	2- 3-  2 7+ -4  2 -2  0
Curve Equation t 67536bu1 [0,0,0,25701,-1794742] 2 67536bu2 [0,0,0,-158619,-17535670] 4 67536bu3 [0,0,0,-930459,331490378] 2 67536bu4 [0,0,0,-2335899,-1373981110] 2
67536bv (2 curves)	0	2- 3- 7+ 67-	2- 3-  4 7+ -4 -6 -6 -4
Curve Equation t 67536bv1 [0,0,0,19399272,-151625331065] 2 67536bv2 [0,0,0,-335312463,-2210017529270] 2
67536bw (4 curves)	0	2- 3- 7- 67+	2- 3- -2 7- -4  2  6  8
Curve Equation t 67536bw1 [0,0,0,534669,-110380174] 2 67536bw2 [0,0,0,-2697411,-983688190] 4 67536bw3 [0,0,0,-19243731,31794571730] 2 67536bw4 [0,0,0,-37864371,-89653661134] 2
67536bx (2 curves)	0	2- 3- 7- 67+	2- 3- -4 7- -4  4 -2 -2
Curve Equation t 67536bx1 [0,0,0,-3027,-77870] 2 67536bx2 [0,0,0,-51267,-4467710] 2
67536by (1 curve)	1	2- 3- 7- 67-	2- 3- -1 7-  0  3  0  4
Curve Equation t Generators 67536by1 [0,0,0,-1683,26514] 1 [25:8:1]
67536bz (1 curve)	1	2- 3- 7- 67-	2- 3-  3 7-  0 -1  8 -8
Curve Equation t Generators 67536bz1 [0,0,0,-11451,-463318] 1 [-67:56:1]
67536ca (1 curve)	1	2- 3- 7- 67-	2- 3- -4 7- -2  4  3 -7
Curve Equation t Generators 67536ca1 [0,0,0,-568272,165021680] 1 [313:4221:1]

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