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	2686a	Isogeny class
Conductor	2686	Conductor
∏ cp	44	Product of Tamagawa factors cp
Δ	1067529340928 = 211 · 174 · 792	Discriminant
Eigenvalues	2-  2  2  0  0  2 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-10447,-412331]	[a1,a2,a3,a4,a6]
j	126095937366490993/1067529340928	j-invariant
L	5.1971580098606	L(r)(E,1)/r!
Ω	0.47246890998732	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21488g2 85952b2 24174c2 67150c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2686a2

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	2	0	0	2	+	8	0	0	0	-4	6	-6	0	4	-6	0	8	-8	14	+	4	-10	2

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Quadratic twists for elliptic curve 2686a2

-4	8	-3	5	17
21488g2	85952b2	24174c2	67150c2	45662s2

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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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