Cremona's table of elliptic curves

4956 = 2² · 3 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 59-	Signs for the Atkin-Lehner involutions
Class	4956c	Isogeny class
Conductor	4956	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-303485616 = -1 · 24 · 38 · 72 · 59	Discriminant
Eigenvalues	2- 3- -2 7- -2  0 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-169,1136]	[a1,a2,a3,a4,a6]
Generators	[11:-27:1]	Generators of the group modulo torsion
j	-33560707072/18967851	j-invariant
L	4.0939098457046	L(r)(E,1)/r!
Ω	1.6006950388544	Real period
R	0.21313188679143	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19824m1 79296e1 14868b1 123900d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4956c1

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	-	-2	0	-2	4	2	2	-8	-10	2	6	0	-6	-	-4	-2	-12	8	16	-12	-12	8

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Quadratic twists for elliptic curve 4956c1

-4	8	-3	5	-7
19824m1	79296e1	14868b1	123900d1	34692h1

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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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