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	50a1 50a2 50a3 50a4	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	0.7131649814283	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	400c 1600j 450b 50b	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 50a

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 50a

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
400c	1600j	450b	50b	2450p	6050bi	8450x	14450l	18050y	26450i	42050bh	48050l	68450bl	84050f	92450bh	110450o

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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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