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	286f	Isogeny class
Conductor	286	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-286 = -1 · 2 · 11 · 13	Discriminant
Eigenvalues	2-  2  1 -3 11- 13- -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,0,-1]	[a1,a2,a3,a4,a6]
j	-1/286	j-invariant
L	2.5074142997366	L(r)(E,1)/r!
Ω	2.5074142997366	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	2288g1 9152d1 2574i1 7150h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 286f1

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
-	2	1	-3	-	-	-6	0	1	-3	10	2	7	-1	-4	6	-5	-11	-1	16	-7	4	4	12	-16

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Quadratic twists for elliptic curve 286f1

-4	8	-3	5	-7	-11	13	17	-19
2288g1	9152d1	2574i1	7150h1	14014i1	3146e1	3718b1	82654k1	103246h1

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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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