Cremona's table of elliptic curves

53 = Prime conductor

Field	Data	Notes
Atkin-Lehner	53+	Signs for the Atkin-Lehner involutions
Conductor	53	Conductor
Count	1	Number of curves in isogeny class
Curves	53a1	Curves in isogeny class
deg	2	Modular degree for the optimal curve
Eigenvalues	-1 -3  0 -4  0 -3 -3 -5	Hecke eigenvalues for primes less than 20
L	0.43586382417786	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	848e 3392k 477a 1325c	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 53a

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	-3	0	-4	0	-3	-3	-5	7	-7	4	5	6	-2	-2	+	-2	-8	-12	1	-4	-1	-1	-14	1

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Quadratic twists for isogeny class 53a

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
848e	3392k	477a	1325c	2597d	6413g	8957b	15317g	19133a	28037c	44573a	50933a	72557a	89093d	97997a	117077a	2809a

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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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