Cremona's table of elliptic curves

5264 = 2⁴ · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 7- 47+	Signs for the Atkin-Lehner involutions
Class	5264k	Isogeny class
Conductor	5264	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	86245376 = 218 · 7 · 47	Discriminant
Eigenvalues	2- -2  2 7-  2  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-152,-620]	[a1,a2,a3,a4,a6]
Generators	[-9:10:1]	Generators of the group modulo torsion
j	95443993/21056	j-invariant
L	3.3179326755973	L(r)(E,1)/r!
Ω	1.3803174727937	Real period
R	2.4037460519005	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	658b1 21056ba1 47376bx1 36848v1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5264k1

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	-	2	2	6	-4	-8	-4	-8	-10	6	-2	+	-14	6	0	14	-16	-2	16	-14	-6	-2

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Quadratic twists for elliptic curve 5264k1

-4	8	-3	-7
658b1	21056ba1	47376bx1	36848v1

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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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