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	250	Product of Tamagawa factors cp
deg	9400	Modular degree for the optimal curve
Δ	-46358174206263296 = -1 · 225 · 135 · 612	Discriminant
Eigenvalues	2- -1  1  3  2 13-  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,16005,10336393]	[a1,a2,a3,a4,a6]
j	453407867428435919/46358174206263296	j-invariant
L	2.7508212087152	L(r)(E,1)/r!
Ω	0.27508212087152	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	12688g1 50752a1 14274k1 39650a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1586d1

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 1586d1

-4	8	-3	5	-7	13	61
12688g1	50752a1	14274k1	39650a1	77714j1	20618e1	96746e1

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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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