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	2584b	Isogeny class
Conductor	2584	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	11245568 = 211 · 172 · 19	Discriminant
Eigenvalues	2- -2  4  2 -4  2 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-816,-9248]	[a1,a2,a3,a4,a6]
j	29376249698/5491	j-invariant
L	1.7863540502691	L(r)(E,1)/r!
Ω	0.89317702513454	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5168b2 20672o2 23256e2 64600c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2584b2

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	2	-4	2	-	-	-2	-2	4	2	12	-4	4	10	0	-8	-4	0	-2	4	4	-10	-12

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Quadratic twists for elliptic curve 2584b2

-4	8	-3	5	-7	17	-19
5168b2	20672o2	23256e2	64600c2	126616q2	43928d2	49096e2

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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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