Cremona's table of elliptic curves

61 = Prime conductor

Field	Data	Notes
Atkin-Lehner	61+	Signs for the Atkin-Lehner involutions
Conductor	61	Conductor
Count	1	Number of curves in isogeny class
Curves	61a1	Curves in isogeny class
deg	2	Modular degree for the optimal curve
Eigenvalues	-1 -2 -3  1 -5  1  4 -4	Hecke eigenvalues for primes less than 20
L	0.48567365142658	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	976b 3904c 549c 1525a	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 61a

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	1	-5	1	4	-4	-9	-6	0	8	5	-8	4	6	9	+	-7	-8	-11	3	4	-4	-14

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Quadratic twists for isogeny class 61a

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	61
976b	3904c	549c	1525a	2989d	7381c	10309a	17629b	22021a	32269a	51301b	58621d	83509b	102541a	112789b	3721a

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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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