Cremona's table of elliptic curves

517 = 11 · 47

Field	Data	Notes
Atkin-Lehner	11+ 47-	Signs for the Atkin-Lehner involutions
Class	517a	Isogeny class
Conductor	517	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-2940179 = -1 · 113 · 472	Discriminant
Eigenvalues	2 -1  3  4 11+  0  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,36,-3]	[a1,a2,a3,a4,a6]
j	5017776128/2940179	j-invariant
L	3.0767217771558	L(r)(E,1)/r!
Ω	1.5383608885779	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8272m1 33088m1 4653c1 12925a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 517a1

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	4	+	0	0	2	1	2	-3	3	-2	-12	-	-10	9	-10	-5	9	-4	-10	4	-13	-15

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Quadratic twists for elliptic curve 517a1

-4	8	-3	5	-7	-11	13	-47
8272m1	33088m1	4653c1	12925a1	25333b1	5687b1	87373d1	24299d1

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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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