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	1586d	Isogeny class
Conductor	1586	Conductor
∏ cp	50	Product of Tamagawa factors cp
Δ	-2.9675065125176E+20	Discriminant
Eigenvalues	2- -1  1  3  2 13-  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3492955,-2647300407]	[a1,a2,a3,a4,a6]
j	-4713056995643685597046321/296750651251759162016	j-invariant
L	2.7508212087152	L(r)(E,1)/r!
Ω	0.055016424174304	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12688g2 50752a2 14274k2 39650a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1586d2

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	1	3	2	-	3	0	4	0	-8	3	2	-1	13	4	0	-	8	-3	4	0	-16	0	8

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Quadratic twists for elliptic curve 1586d2

-4	8	-3	5	-7	13	61
12688g2	50752a2	14274k2	39650a2	77714j2	20618e2	96746e2

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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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