Cremona's table of elliptic curves

650 = 2 · 5² · 13

Class	r	Atkin-Lehner	Eigenvalues
650a (4 curves)	1	2+ 5+ 13+	2+  0 5+  0  0 13+ -2 -8
Curve Equation t Generators 650a1 [1,-1,0,-167,-259] 2 [-11:18:1] 650a2 [1,-1,0,-2167,-38259] 4 [-27:18:1] 650a3 [1,-1,0,-34667,-2475759] 2 [399:6663:1] 650a4 [1,-1,0,-1667,-56759] 2 [84:583:1]
650b (2 curves)	1	2+ 5+ 13+	2+  2 5+ -5 -3 13+ -3 -4
Curve Equation t Generators 650b1 [1,1,0,-130,-780] 1 [84:726:1] 650b2 [1,1,0,-11330,-468940] 1 [124:166:1]
650c (1 curve)	1	2+ 5+ 13+	2+ -3 5+  0 -3 13+  7  1
Curve Equation t Generators 650c1 [1,-1,0,-22,46] 1 [5:4:1]
650d (1 curve)	0	2+ 5+ 13-	2+  1 5+  4  1 13-  7 -3
Curve Equation t 650d1 [1,0,1,299,22048] 1
650e (2 curves)	0	2+ 5+ 13-	2+ -2 5+  4 -2 13- -2  6
Curve Equation t 650e1 [1,0,1,-21026,-1175052] 2 650e2 [1,0,1,-19026,-1407052] 2
650f (2 curves)	0	2+ 5+ 13-	2+  3 5+ -1 -2 13-  3  6
Curve Equation t 650f1 [1,-1,0,-67,341] 1 650f2 [1,-1,0,-5317,-162409] 1
650g (2 curves)	1	2+ 5- 13-	2+ -2 5- -1  3 13-  3 -4
Curve Equation t Generators 650g1 [1,0,1,-26,48] 3 [-3:11:1] 650g2 [1,0,1,99,248] 1 [11:-58:1]
650h (3 curves)	0	2- 5+ 13+	2- -1 5+  1  6 13+  3  2
Curve Equation t 650h1 [1,1,1,12,31] 1 650h2 [1,1,1,-113,-969] 1 650h3 [1,1,1,-11488,-478719] 1
650i (2 curves)	0	2- 5+ 13+	2-  2 5+  1  3 13+ -3 -4
Curve Equation t 650i1 [1,1,1,-638,6031] 1 650i2 [1,1,1,2487,31031] 1
650j (4 curves)	0	2- 5+ 13+	2-  2 5+  4 -6 13+  6  2
Curve Equation t 650j1 [1,1,1,-813,8531] 2 650j2 [1,1,1,-313,19531] 2 650j3 [1,1,1,-5188,-140219] 2 650j4 [1,1,1,2812,-524219] 2
650k (1 curve)	1	2- 5- 13+	2- -1 5- -4  1 13+ -7 -3
Curve Equation t Generators 650k1 [1,1,1,12,181] 1 [25:117:1]
650l (2 curves)	0	2- 5- 13-	2- -2 5-  5 -3 13-  3 -4
Curve Equation t 650l1 [1,0,0,-3263,-90983] 3 650l2 [1,0,0,-283263,-58050983] 1
650m (1 curve)	0	2- 5- 13-	2-  3 5-  0 -3 13- -7  1
Curve Equation t 650m1 [1,-1,1,-555,5197] 1

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

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