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	5264i	Isogeny class
Conductor	5264	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-5519704064 = -1 · 224 · 7 · 47	Discriminant
Eigenvalues	2-  1 -1 7-  5  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,384,2228]	[a1,a2,a3,a4,a6]
Generators	[4:62:1]	Generators of the group modulo torsion
j	1524845951/1347584	j-invariant
L	4.4415090707777	L(r)(E,1)/r!
Ω	0.88203578819133	Real period
R	2.5177601239317	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	658d1 21056w1 47376br1 36848t1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5264i1

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	-	5	2	-6	-4	4	-10	-2	5	3	1	+	-5	-3	-12	-4	-4	-5	4	1	12	-2

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Quadratic twists for elliptic curve 5264i1

-4	8	-3	-7
658d1	21056w1	47376br1	36848t1

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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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