Cremona's table of elliptic curves

493 = 17 · 29

Field	Data	Notes
Atkin-Lehner	17- 29+	Signs for the Atkin-Lehner involutions
Class	493a	Isogeny class
Conductor	493	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1872	Modular degree for the optimal curve
Δ	-246621481589773 = -1 · 17 · 299	Discriminant
Eigenvalues	-1  0 -2 -5  0  7 17-  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-7741,801682]	[a1,a2,a3,a4,a6]
j	-51293497953529377/246621481589773	j-invariant
L	0.48177022318862	L(r)(E,1)/r!
Ω	0.48177022318862	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7888f1 31552k1 4437f1 12325a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 493a1

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
-1	0	-2	-5	0	7	-	5	4	+	4	-11	3	-5	9	-3	6	-1	4	5	3	-6	14	-8	2

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Quadratic twists for elliptic curve 493a1

-4	8	-3	5	-7	-11	13	17	29
7888f1	31552k1	4437f1	12325a1	24157b1	59653b1	83317d1	8381c1	14297b1

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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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