Cremona's table of elliptic curves

496 = 2⁴ · 31

Field	Data	Notes
Atkin-Lehner	2+ 31-	Signs for the Atkin-Lehner involutions
Class	496c	Isogeny class
Conductor	496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-31744 = -1 · 210 · 31	Discriminant
Eigenvalues	2+  2  2  0 -2  4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8,0]	[a1,a2,a3,a4,a6]
j	48668/31	j-invariant
L	2.3037511398078	L(r)(E,1)/r!
Ω	2.3037511398078	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	248b1 1984l1 4464j1 12400i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 496c1

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
+	2	2	0	-2	4	6	-4	0	-4	-	4	-10	2	8	4	0	0	-12	0	2	-12	14	-14	14

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Quadratic twists for elliptic curve 496c1

-4	8	-3	5	-7	-11	13	-31
248b1	1984l1	4464j1	12400i1	24304e1	60016d1	83824c1	15376n1

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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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