Cremona's table of elliptic curves

496 = 2⁴ · 31

Field	Data	Notes
Atkin-Lehner	2- 31-	Signs for the Atkin-Lehner involutions
Class	496f	Isogeny class
Conductor	496	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	15745024 = 214 · 312	Discriminant
Eigenvalues	2-  0 -2  0  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-331,-2310]	[a1,a2,a3,a4,a6]
Generators	[39:210:1]	Generators of the group modulo torsion
j	979146657/3844	j-invariant
L	1.7961902527622	L(r)(E,1)/r!
Ω	1.1195541660226	Real period
R	3.2087598925981	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	62a2 1984j2 4464x2 12400r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 496f2

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	-2	0	0	2	-6	-4	-8	2	-	10	-6	-8	8	-6	12	-6	12	-8	10	8	-8	-6	2

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Quadratic twists for elliptic curve 496f2

-4	8	-3	5	-7	-11	13	-31
62a2	1984j2	4464x2	12400r2	24304n2	60016n2	83824k2	15376u2

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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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