Cremona's table of elliptic curves

50 = 2 · 5²

Field	Data	Notes
Atkin-Lehner	2- 5+	Signs for the Atkin-Lehner involutions
Conductor	50	Conductor
Count	4	Number of curves in isogeny class
Curves	50b1 50b2 50b3 50b4	Curves in isogeny class
deg	2	Modular degree for the optimal curve
Eigenvalues	2- -1 5+ -2 -3  4  3  5	Hecke eigenvalues for primes less than 20
L	0.95681122658763	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	400b 1600c 450d 50a	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 50b

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-1	+	-2	-3	4	3	5	-6	0	2	-2	-3	4	-12	-6	0	2	13	12	-11	-10	9	15	-2

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Quadratic twists for isogeny class 50b

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
400b	1600c	450d	50a	2450v	6050g	8450d	14450t	18050f	26450o	42050f	48050v	68450d	84050j	92450g	110450bc

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

Part of Computational Number Theory
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