Cremona's table of elliptic curves

1586 = 2 · 13 · 61

Field	Data	Notes
Atkin-Lehner	2+ 13+ 61+	Signs for the Atkin-Lehner involutions
Class	1586a	Isogeny class
Conductor	1586	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	616	Modular degree for the optimal curve
Δ	-99067904 = -1 · 211 · 13 · 612	Discriminant
Eigenvalues	2+ -1  3  1  2 13+ -5 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-111,613]	[a1,a2,a3,a4,a6]
Generators	[-3:32:1]	Generators of the group modulo torsion
j	-153388121977/99067904	j-invariant
L	2.1458400767391	L(r)(E,1)/r!
Ω	1.7494668105808	Real period
R	0.61328401995427	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	12688c1 50752g1 14274q1 39650h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1586a1

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	3	1	2	+	-5	-4	-8	-8	-8	1	10	-9	7	0	-4	+	8	-9	16	-12	-4	12	8

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Quadratic twists for elliptic curve 1586a1

-4	8	-3	5	-7	13	61
12688c1	50752g1	14274q1	39650h1	77714h1	20618g1	96746h1

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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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