Cremona's table of elliptic curves

517 = 11 · 47

Field	Data	Notes
Atkin-Lehner	11- 47-	Signs for the Atkin-Lehner involutions
Class	517c	Isogeny class
Conductor	517	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	-6494855411 = -1 · 113 · 474	Discriminant
Eigenvalues	2 -1 -3 -2 11-  0 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-52,-3863]	[a1,a2,a3,a4,a6]
Generators	[170:513:8]	Generators of the group modulo torsion
j	-15851081728/6494855411	j-invariant
L	2.6598825790626	L(r)(E,1)/r!
Ω	0.59941339986001	Real period
R	0.36978966709839	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8272g1 33088j1 4653a1 12925b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 517c1

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
2	-1	-3	-2	-	0	-6	8	-5	-4	3	3	4	-6	-	2	-3	8	-11	-3	-4	2	-14	-1	-15

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Quadratic twists for elliptic curve 517c1

-4	8	-3	5	-7	-11	13	-47
8272g1	33088j1	4653a1	12925b1	25333c1	5687c1	87373b1	24299b1

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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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