Cremona's table of elliptic curves

651 = 3 · 7 · 31

Class	r	Atkin-Lehner	Eigenvalues
651a (2 curves)	0	3+ 7- 31+	1 3+ -2 7-  2  4  8 -4
Curve Equation t 651a1 [1,1,0,-5596,-164045] 2 651a2 [1,1,0,-89631,-10365894] 2
651b (2 curves)	0	3+ 7- 31+	1 3+  4 7-  2 -2  2  8
Curve Equation t 651b1 [1,1,0,-3,0] 2 651b2 [1,1,0,12,15] 2
651c (2 curves)	1	3- 7+ 31-	1 3- -2 7+ -2 -4  0 -4
Curve Equation t Generators 651c1 [1,0,1,3,-5] 2 [5:9:1] 651c2 [1,0,1,-32,-61] 2 [-3:4:1]
651d (4 curves)	1	3- 7- 31+	-1 3- -2 7-  0 -6  6 -4
Curve Equation t Generators 651d1 [1,0,0,36,-81] 4 [3:6:1] 651d2 [1,0,0,-209,-816] 4 [-11:19:1] 651d3 [1,0,0,-3044,-64887] 2 [-32:19:1] 651d4 [1,0,0,-1294,17195] 2 [-37:140:1]
651e (3 curves)	0	3- 7- 31-	0 3- -3 7-  0  5  0  2
Curve Equation t 651e1 [0,1,1,23,-83] 3 651e2 [0,1,1,-1057,-13610] 3 651e3 [0,1,1,-85687,-9682913] 1

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

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