Cremona's table of elliptic curves

5096 = 2³ · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	5096f	Isogeny class
Conductor	5096	Conductor
∏ cp	112	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	-13229082095547136 = -1 · 28 · 77 · 137	Discriminant
Eigenvalues	2+ -2 -3 7-  0 13-  2 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,52463,-3020781]	[a1,a2,a3,a4,a6]
Generators	[79:1274:1]	Generators of the group modulo torsion
j	530208386048/439239619	j-invariant
L	1.9768459166477	L(r)(E,1)/r!
Ω	0.22031706127333	Real period
R	0.080113677388657	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	10192j1 40768v1 45864bv1 127400bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5096f1

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	-3	-	0	-	2	-5	1	-5	3	-6	2	1	-3	11	8	10	2	14	7	13	1	11	-5

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Quadratic twists for elliptic curve 5096f1

-4	8	-3	5	-7	13
10192j1	40768v1	45864bv1	127400bn1	728b1	66248x1

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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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