Cremona's table of elliptic curves

6413 = 11² · 53

Class	r	Atkin-Lehner	Eigenvalues
6413a (2 curves)	1	11+ 53+	1 -2 -2 -4 11+  0 -4  4
Curve Equation t Generators 6413a1 [1,0,1,8,9] 2 [3:6:1] 6413a2 [1,0,1,-47,75] 2 [-1:11:1]
6413b (2 curves)	1	11+ 53+	-1 -2 -2  4 11+  0  4 -4
Curve Equation t Generators 6413b1 [1,0,0,1026,-11285] 2 [417:2252:27] 6413b2 [1,0,0,-5629,-105786] 2 [99:507:1]
6413c (1 curve)	0	11+ 53-	0  3  1  4 11+  0  4  8
Curve Equation t 6413c1 [0,0,1,-22,-4931] 1
6413d (1 curve)	0	11+ 53-	0  3  1 -4 11+  0 -4 -8
Curve Equation t 6413d1 [0,0,1,-2662,6562828] 1
6413e (1 curve)	0	11+ 53-	2  1 -1  2 11+  6  4  4
Curve Equation t 6413e1 [0,1,1,444,-123623] 1
6413f (1 curve)	2	11+ 53-	-2  1 -1 -2 11+ -6 -4 -4
Curve Equation t Generators 6413f1 [0,1,1,4,94] 1 [-4:5:1]&[8:26:1]
6413g (1 curve)	0	11- 53+	1 -3  0  4 11-  3  3  5
Curve Equation t 6413g1 [1,-1,0,38,-467] 1
6413h (1 curve)	0	11- 53+	-1 -1  4 -4 11- -1 -1  3
Curve Equation t 6413h1 [1,1,1,-43381,4568136] 1
6413i (1 curve)	0	11- 53+	-2  3 -3 -2 11-  0 -6  8
Curve Equation t 6413i1 [0,0,1,59411,3464260] 1
6413j (1 curve)	1	11- 53-	-2  1  3  0 11- -4  0  4
Curve Equation t Generators 6413j1 [0,1,1,686,9114] 1 [216:3206:1]

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

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