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	5096g	Isogeny class
Conductor	5096	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	15588021904 = 24 · 78 · 132	Discriminant
Eigenvalues	2- -1  1 7+  5 13-  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-800,-6047]	[a1,a2,a3,a4,a6]
Generators	[-16:49:1]	Generators of the group modulo torsion
j	614656/169	j-invariant
L	3.5060388983926	L(r)(E,1)/r!
Ω	0.91616918225708	Real period
R	0.31890388135474	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	10192c1 40768a1 45864g1 127400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5096g1

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	-	3	-5	-3	-6	-3	-3	6	-8	-9	-5	1	7	13	0	9	5	-12	-11	10

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Quadratic twists for elliptic curve 5096g1

-4	8	-3	5	-7	13
10192c1	40768a1	45864g1	127400b1	5096i1	66248a1

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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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