Cremona's table of elliptic curves

2686 = 2 · 17 · 79

Field	Data	Notes
Atkin-Lehner	2- 17+ 79-	Signs for the Atkin-Lehner involutions
Class	2686d	Isogeny class
Conductor	2686	Conductor
∏ cp	44	Product of Tamagawa factors cp
deg	5280	Modular degree for the optimal curve
Δ	445003071488 = 222 · 17 · 792	Discriminant
Eigenvalues	2-  2  0 -4 -2 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2893,-51773]	[a1,a2,a3,a4,a6]
Generators	[247:3668:1]	Generators of the group modulo torsion
j	2677801592364625/445003071488	j-invariant
L	5.5267956377173	L(r)(E,1)/r!
Ω	0.65831936041161	Real period
R	0.76321007292124	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21488f1 85952g1 24174e1 67150g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2686d1

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	0	-4	-2	-6	+	4	-8	-4	4	0	-10	12	8	6	4	8	0	-8	-6	-	0	-6	-18

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Quadratic twists for elliptic curve 2686d1

-4	8	-3	5	17
21488f1	85952g1	24174e1	67150g1	45662m1

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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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