Cremona's table of elliptic curves

51264 = 2⁶ · 3² · 89

Class	r	Atkin-Lehner	Eigenvalues
51264a (1 curve)	1	2+ 3+ 89+	2+ 3+  2  0 -6  4 -2 -4
Curve Equation t Generators 51264a1 [0,0,0,-384,-2912] 1 [1522:20877:8]
51264b (1 curve)	1	2+ 3+ 89+	2+ 3+  2  2 -4  2 -4  2
Curve Equation t Generators 51264b1 [0,0,0,6,-18] 1 [18:21:8]
51264c (1 curve)	1	2+ 3+ 89+	2+ 3+  2 -2  4  2 -4 -2
Curve Equation t Generators 51264c1 [0,0,0,6,18] 1 [1:5:1]
51264d (1 curve)	0	2+ 3+ 89-	2+ 3+ -2  0  6  4  2 -4
Curve Equation t 51264d1 [0,0,0,-3456,78624] 1
51264e (1 curve)	0	2+ 3+ 89-	2+ 3+ -2  2  4  2  4  2
Curve Equation t 51264e1 [0,0,0,54,486] 1
51264f (1 curve)	2	2+ 3+ 89-	2+ 3+ -2 -2 -4  2  4 -2
Curve Equation t Generators 51264f1 [0,0,0,54,-486] 1 [9:27:1]&[241:3743:1]
51264g (1 curve)	0	2+ 3- 89+	2+ 3- -1  0  0  4  1  5
Curve Equation t 51264g1 [0,0,0,132,1456] 1
51264h (2 curves)	0	2+ 3- 89+	2+ 3-  2  0  0  4 -2  2
Curve Equation t 51264h1 [0,0,0,-25644,-1361360] 2 51264h2 [0,0,0,-394284,-95290832] 2
51264i (2 curves)	0	2+ 3- 89+	2+ 3-  2  2 -4 -4  2  8
Curve Equation t 51264i1 [0,0,0,-1044,12960] 2 51264i2 [0,0,0,-684,22032] 2
51264j (2 curves)	0	2+ 3- 89+	2+ 3-  2 -2  4 -4  2 -8
Curve Equation t 51264j1 [0,0,0,-1044,-12960] 2 51264j2 [0,0,0,-684,-22032] 2
51264k (2 curves)	2	2+ 3- 89+	2+ 3-  2 -4  0 -4 -2 -2
Curve Equation t Generators 51264k1 [0,0,0,-1164,14960] 2 [-28:160:1]&[-10:160:1] 51264k2 [0,0,0,-2604,-29392] 2 [-26:144:1]&[-19:115:1]
51264l (2 curves)	2	2+ 3- 89+	2+ 3- -2  2 -4 -2 -6  2
Curve Equation t Generators 51264l1 [0,0,0,-876,-7760] 2 [-19:45:1]&[-12:32:1] 51264l2 [0,0,0,2004,-48080] 2 [38:288:1]&[276:4640:1]
51264m (2 curves)	0	2+ 3- 89+	2+ 3- -2 -2 -4  0  2  4
Curve Equation t 51264m1 [0,0,0,-8076,-235280] 2 51264m2 [0,0,0,14964,-1331984] 2
51264n (4 curves)	0	2+ 3- 89+	2+ 3- -2  4 -4 -2 -2 -4
Curve Equation t 51264n1 [0,0,0,-86556,-9801520] 2 51264n2 [0,0,0,-87276,-9630160] 4 51264n3 [0,0,0,29364,-33471376] 2 51264n4 [0,0,0,-215436,25178096] 2
51264o (1 curve)	0	2+ 3- 89+	2+ 3-  4 -2  2 -2 -8  8
Curve Equation t 51264o1 [0,0,0,-48,2720] 1
51264p (1 curve)	0	2+ 3- 89+	2+ 3-  4 -2  2 -6 -4  4
Curve Equation t 51264p1 [0,0,0,-15888,-1354790] 1
51264q (1 curve)	0	2+ 3- 89+	2+ 3-  4  4  0  0 -6 -2
Curve Equation t 51264q1 [0,0,0,-5898,-174350] 1
51264r (1 curve)	0	2+ 3- 89+	2+ 3-  4 -4  0  0 -6  2
Curve Equation t 51264r1 [0,0,0,-5898,174350] 1
51264s (2 curves)	1	2+ 3- 89-	2+ 3-  0  2  6 -2  0  4
Curve Equation t Generators 51264s1 [0,0,0,-120,-718] 1 [381:539:27] 51264s2 [0,0,0,960,9866] 1 [95:979:1]
51264t (1 curve)	1	2+ 3- 89-	2+ 3- -1 -4 -2 -2 -3  5
Curve Equation t Generators 51264t1 [0,0,0,-588,-8336] 1 [30:32:1]
51264u (2 curves)	1	2+ 3- 89-	2+ 3-  3 -4 -6 -2 -3 -5
Curve Equation t Generators 51264u1 [0,0,0,3444,393968] 1 [-726:14336:27] 51264u2 [0,0,0,-319116,69421808] 1 [-418:11392:1]
51264v (1 curve)	0	2- 3+ 89+	2- 3+  2  0  6  4 -2  4
Curve Equation t 51264v1 [0,0,0,-384,2912] 1
51264w (1 curve)	1	2- 3+ 89-	2- 3+ -2  0 -6  4  2  4
Curve Equation t Generators 51264w1 [0,0,0,-3456,-78624] 1 [46920:313227:512]
51264x (1 curve)	1	2- 3- 89+	2- 3- -1  0  0  4  1 -5
Curve Equation t Generators 51264x1 [0,0,0,132,-1456] 1 [14:56:1]
51264y (2 curves)	1	2- 3- 89+	2- 3-  2  0  0  4 -2 -2
Curve Equation t Generators 51264y1 [0,0,0,-25644,1361360] 2 [9340:902520:1] 51264y2 [0,0,0,-394284,95290832] 2 [-694:5888:1]
51264z (2 curves)	1	2- 3- 89+	2- 3-  2  4  0 -4 -2  2
Curve Equation t Generators 51264z1 [0,0,0,-1164,-14960] 2 [860:25200:1] 51264z2 [0,0,0,-2604,29392] 2 [-54:112:1]
51264ba (2 curves)	1	2- 3- 89+	2- 3- -2  2  4  0  2 -4
Curve Equation t Generators 51264ba1 [0,0,0,-8076,235280] 2 [-64:700:1] 51264ba2 [0,0,0,14964,1331984] 2 [226:4032:1]
51264bb (2 curves)	1	2- 3- 89+	2- 3- -2 -2  4 -2 -6 -2
Curve Equation t Generators 51264bb1 [0,0,0,-876,7760] 2 [-22:128:1] 51264bb2 [0,0,0,2004,48080] 2 [-4:200:1]
51264bc (4 curves)	1	2- 3- 89+	2- 3- -2 -4  4 -2 -2  4
Curve Equation t Generators 51264bc1 [0,0,0,-86556,9801520] 2 [152:396:1] 51264bc2 [0,0,0,-87276,9630160] 4 [144:220:1] 51264bc3 [0,0,0,29364,33471376] 2 [-286:1296:1] 51264bc4 [0,0,0,-215436,-25178096] 2 [-46080:254452:125]
51264bd (1 curve)	1	2- 3- 89+	2- 3-  4  2 -2 -2 -8 -8
Curve Equation t Generators 51264bd1 [0,0,0,-48,-2720] 1 [130:225:8]
51264be (1 curve)	1	2- 3- 89+	2- 3-  4  2 -2 -6 -4 -4
Curve Equation t Generators 51264be1 [0,0,0,-15888,1354790] 1 [20455:221389:125]
51264bf (1 curve)	0	2- 3- 89-	2- 3-  0  0  0 -4 -6  6
Curve Equation t 51264bf1 [0,0,0,330,3962] 1
51264bg (1 curve)	2	2- 3- 89-	2- 3-  0  0  0 -4 -6 -6
Curve Equation t Generators 51264bg1 [0,0,0,330,-3962] 1 [17:81:1]&[113:1215:1]
51264bh (2 curves)	2	2- 3- 89-	2- 3-  0 -2 -6 -2  0 -4
Curve Equation t Generators 51264bh1 [0,0,0,-120,718] 1 [-13:9:1]&[11:27:1] 51264bh2 [0,0,0,960,-9866] 1 [83:-801:1]&[2338:40185:8]
51264bi (1 curve)	0	2- 3- 89-	2- 3- -1  4  2  2 -3 -7
Curve Equation t 51264bi1 [0,0,0,-63,216] 1
51264bj (1 curve)	0	2- 3- 89-	2- 3- -1  4  2 -2 -3 -5
Curve Equation t 51264bj1 [0,0,0,-588,8336] 1
51264bk (1 curve)	0	2- 3- 89-	2- 3- -1 -4 -2  2 -3  7
Curve Equation t 51264bk1 [0,0,0,-63,-216] 1
51264bl (2 curves)	0	2- 3- 89-	2- 3-  3  4  6 -2 -3  5
Curve Equation t 51264bl1 [0,0,0,3444,-393968] 1 51264bl2 [0,0,0,-319116,-69421808] 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