Cremona's table of elliptic curves

5056 = 2⁶ · 79

Field	Data	Notes
Atkin-Lehner	2- 79-	Signs for the Atkin-Lehner involutions
Class	5056s	Isogeny class
Conductor	5056	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	1294336 = 214 · 79	Discriminant
Eigenvalues	2- -1 -1 -3  2  1  4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-721,7697]	[a1,a2,a3,a4,a6]
Generators	[17:8:1]	Generators of the group modulo torsion
j	2533446736/79	j-invariant
L	2.6458456379797	L(r)(E,1)/r!
Ω	2.5340493252651	Real period
R	0.26102941363453	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	5056c1 1264f1 45504bs1 126400bz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5056s1

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	-1	-3	2	1	4	6	-6	-8	4	8	-10	4	9	2	5	6	-10	1	6	-	0	9	-11

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Quadratic twists for elliptic curve 5056s1

-4	8	-3	5
5056c1	1264f1	45504bs1	126400bz1

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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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