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	1586c	Isogeny class
Conductor	1586	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4896	Modular degree for the optimal curve
Δ	193380548608 = 216 · 13 · 613	Discriminant
Eigenvalues	2-  0  2  4  4 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-61389,5869685]	[a1,a2,a3,a4,a6]
j	25585196494633455393/193380548608	j-invariant
L	3.610884995955	L(r)(E,1)/r!
Ω	0.90272124898876	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12688b1 50752e1 14274e1 39650c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1586c1

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	2	4	4	+	-6	6	2	2	4	-6	-6	-2	-2	-6	-4	+	-8	4	2	14	-6	6	2

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Quadratic twists for elliptic curve 1586c1

-4	8	-3	5	-7	13	61
12688b1	50752e1	14274e1	39650c1	77714o1	20618a1	96746b1

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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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