Cremona's table of elliptic curves

496 = 2⁴ · 31

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	496a	Isogeny class
Conductor	496	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-496 = -1 · 24 · 31	Discriminant
Eigenvalues	2+  0 -3  3 -2 -4  0 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	6912/31	j-invariant
L	1.7858094938692	L(r)(E,1)/r!
Ω	3.7499429780943	Real period
R	0.47622310640487	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	248c1 1984g1 4464e1 12400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 496a1

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	-3	3	-2	-4	0	-1	-4	-6	+	-10	7	10	-12	-4	-3	12	12	13	2	-6	-6	-10	1

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Quadratic twists for elliptic curve 496a1

-4	8	-3	5	-7	-11	13	-31
248c1	1984g1	4464e1	12400c1	24304h1	60016a1	83824e1	15376f1

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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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