Cremona's table of elliptic curves

8585 = 5 · 17 · 101

Field	Data	Notes
Atkin-Lehner	5+ 17+ 101+	Signs for the Atkin-Lehner involutions
Class	8585a	Isogeny class
Conductor	8585	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2176	Modular degree for the optimal curve
Δ	1073125 = 54 · 17 · 101	Discriminant
Eigenvalues	0 -1 5+ -5 -3  3 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-331,2431]	[a1,a2,a3,a4,a6]
Generators	[13:12:1]	Generators of the group modulo torsion
j	4022713483264/1073125	j-invariant
L	1.4587156621693	L(r)(E,1)/r!
Ω	2.6958230427018	Real period
R	0.27055107829098	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	77265h1 42925f1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 8585a1

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
0	-1	+	-5	-3	3	+	1	-8	2	-6	-6	2	5	0	-6	6	10	0	0	-11	14	10	8	2

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Quadratic twists for elliptic curve 8585a1

-3	5
77265h1	42925f1

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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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