Cremona's table of elliptic curves

2585 = 5 · 11 · 47

Field	Data	Notes
Atkin-Lehner	5- 11- 47+	Signs for the Atkin-Lehner involutions
Class	2585b	Isogeny class
Conductor	2585	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	704	Modular degree for the optimal curve
Δ	-3440635 = -1 · 5 · 114 · 47	Discriminant
Eigenvalues	-2  2 5- -2 11-  1  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,10,-92]	[a1,a2,a3,a4,a6]
Generators	[7:16:1]	Generators of the group modulo torsion
j	99897344/3440635	j-invariant
L	2.3720751919299	L(r)(E,1)/r!
Ω	1.2061955051932	Real period
R	0.49164401245838	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	41360m1 23265o1 12925e1 126665b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2585b1

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	-	-2	-	1	0	0	-9	0	-10	2	-6	11	+	-12	11	3	-8	-13	7	-9	-6	15	12

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Quadratic twists for elliptic curve 2585b1

-4	-3	5	-7	-11	-47
41360m1	23265o1	12925e1	126665b1	28435j1	121495b1

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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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