Cremona's table of elliptic curves

2584 = 2³ · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	2584a	Isogeny class
Conductor	2584	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1571072 = 28 · 17 · 192	Discriminant
Eigenvalues	2- -2 -2  0  0  2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-84,-320]	[a1,a2,a3,a4,a6]
Generators	[-6:2:1]	Generators of the group modulo torsion
j	259108432/6137	j-invariant
L	2.0115454703009	L(r)(E,1)/r!
Ω	1.5777071112559	Real period
R	0.63749014501799	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5168a2 20672e2 23256h2 64600j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2584a2

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	0	2	+	-	0	0	6	8	0	4	-8	-6	12	-10	4	-2	14	6	-12	-2	-16

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Quadratic twists for elliptic curve 2584a2

-4	8	-3	5	-7	17	-19
5168a2	20672e2	23256h2	64600j2	126616u2	43928c2	49096b2

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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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