Cremona's table of elliptic curves

2656 = 2⁵ · 83

Field	Data	Notes
Atkin-Lehner	2- 83-	Signs for the Atkin-Lehner involutions
Class	2656f	Isogeny class
Conductor	2656	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-36594368 = -1 · 26 · 833	Discriminant
Eigenvalues	2- -3 -2 -3 -3  0  5  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-61,-344]	[a1,a2,a3,a4,a6]
Generators	[31:166:1]	Generators of the group modulo torsion
j	-392223168/571787	j-invariant
L	1.4394783895666	L(r)(E,1)/r!
Ω	0.81162719996235	Real period
R	0.29559515124542	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	2656c1 5312k1 23904d1 66400d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2656f1

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
-	-3	-2	-3	-3	0	5	0	0	-1	9	7	-2	0	6	8	-9	-1	0	6	6	0	-	-14	-6

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Quadratic twists for elliptic curve 2656f1

-4	8	-3	5
2656c1	5312k1	23904d1	66400d1

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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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