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	5096h	Isogeny class
Conductor	5096	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-463186936576 = -1 · 28 · 77 · 133	Discriminant
Eigenvalues	2-  0  1 7-  2 13+  0  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3332,80948]	[a1,a2,a3,a4,a6]
Generators	[28:98:1]	Generators of the group modulo torsion
j	-135834624/15379	j-invariant
L	3.9928639133239	L(r)(E,1)/r!
Ω	0.91078077341539	Real period
R	1.0960002752229	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	10192d1 40768be1 45864j1 127400g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5096h1

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
-	0	1	-	2	+	0	7	-3	-9	-5	-8	10	5	-7	3	0	-6	-10	4	11	-11	-11	3	15

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Quadratic twists for elliptic curve 5096h1

-4	8	-3	5	-7	13
10192d1	40768be1	45864j1	127400g1	728c1	66248d1

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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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