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	16	Product of Tamagawa factors cp
Δ	7565484032 = 213 · 314	Discriminant
Eigenvalues	2-  0 -2  0  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-491,154]	[a1,a2,a3,a4,a6]
Generators	[-3:40:1]	Generators of the group modulo torsion
j	3196010817/1847042	j-invariant
L	1.7961902527622	L(r)(E,1)/r!
Ω	1.1195541660226	Real period
R	1.604379946299	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	62a3 1984j4 4464x3 12400r4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 496f4

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 496f4

-4	8	-3	5	-7	-11	13	-31
62a3	1984j4	4464x3	12400r4	24304n3	60016n3	83824k3	15376u3

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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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