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	1586b	Isogeny class
Conductor	1586	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	984	Modular degree for the optimal curve
Δ	-16350074 = -1 · 2 · 133 · 612	Discriminant
Eigenvalues	2+  3  3 -3  2 13+ -5  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,62,38]	[a1,a2,a3,a4,a6]
j	26118765063/16350074	j-invariant
L	2.7275029457733	L(r)(E,1)/r!
Ω	1.3637514728866	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	12688e1 50752d1 14274s1 39650j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1586b1

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
+	3	3	-3	2	+	-5	8	0	4	0	1	6	-13	11	8	0	-	4	3	-4	4	-12	-8	-12

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Quadratic twists for elliptic curve 1586b1

-4	8	-3	5	-7	13	61
12688e1	50752d1	14274s1	39650j1	77714g1	20618m1	96746j1

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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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