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	5264f	Isogeny class
Conductor	5264	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-264126464 = -1 · 214 · 73 · 47	Discriminant
Eigenvalues	2- -1  3 7+ -3  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,56,-784]	[a1,a2,a3,a4,a6]
Generators	[10:26:1]	Generators of the group modulo torsion
j	4657463/64484	j-invariant
L	3.6267171774103	L(r)(E,1)/r!
Ω	0.85459438224134	Real period
R	2.1218938789994	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	658c1 21056q1 47376bg1 36848m1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5264f1

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	3	+	-3	2	0	-2	0	0	4	-1	-3	1	-	9	-9	-4	-8	6	-7	-2	-9	0	-16

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Quadratic twists for elliptic curve 5264f1

-4	8	-3	-7
658c1	21056q1	47376bg1	36848m1

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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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