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	286b	Isogeny class
Conductor	286	Conductor
∏ cp	26	Product of Tamagawa factors cp
deg	104	Modular degree for the optimal curve
Δ	-12886016 = -1 · 213 · 112 · 13	Discriminant
Eigenvalues	2- -1 -3 -5 11+ 13-  7  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,13,177]	[a1,a2,a3,a4,a6]
Generators	[19:-98:1]	Generators of the group modulo torsion
j	241804367/12886016	j-invariant
L	1.6606489871013	L(r)(E,1)/r!
Ω	1.7061664867551	Real period
R	0.037435452744113	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	2288k1 9152i1 2574p1 7150c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 286b1

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	-3	-5	+	-	7	0	-4	-8	0	-3	-8	-5	-3	2	-14	8	0	-5	16	-6	-4	0	0

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Quadratic twists for elliptic curve 286b1

-4	8	-3	5	-7	-11	13	17	-19
2288k1	9152i1	2574p1	7150c1	14014f1	3146d1	3718f1	82654o1	103246b1

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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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