Cremona's table of elliptic curves

498 = 2 · 3 · 83

Field	Data	Notes
Atkin-Lehner	2+ 3- 83+	Signs for the Atkin-Lehner involutions
Class	498a	Isogeny class
Conductor	498	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-124002 = -1 · 2 · 32 · 832	Discriminant
Eigenvalues	2+ 3-  2  4  0  0 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,5,-16]	[a1,a2,a3,a4,a6]
j	18191447/124002	j-invariant
L	1.6473197161008	L(r)(E,1)/r!
Ω	1.6473197161008	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	3984d2 15936e2 1494e2 12450r2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 498a2

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

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Quadratic twists for elliptic curve 498a2

-4	8	-3	5	-7	-11	13	-83
3984d2	15936e2	1494e2	12450r2	24402e2	60258bf2	84162ba2	41334k2

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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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