Cremona's table of elliptic curves

286 = 2 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	286c	Isogeny class
Conductor	286	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-12584 = -1 · 23 · 112 · 13	Discriminant
Eigenvalues	2+ -1 -1  1 11+ 13+ -1 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-33,61]	[a1,a2,a3,a4,a6]
Generators	[1:5:1]	Generators of the group modulo torsion
j	-4165509529/12584	j-invariant
L	1.0773574603489	L(r)(E,1)/r!
Ω	4.0135805232866	Real period
R	0.13421400842691	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	2288h1 9152k1 2574w1 7150r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 286c1

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	1	+	+	-1	-4	-8	-8	0	7	-8	11	-1	2	14	-8	8	9	-4	2	0	-4	8

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Quadratic twists for elliptic curve 286c1

-4	8	-3	5	-7	-11	13	17	-19
2288h1	9152k1	2574w1	7150r1	14014c1	3146p1	3718p1	82654c1	103246o1

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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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