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	2686b	Isogeny class
Conductor	2686	Conductor
∏ cp	52	Product of Tamagawa factors cp
Δ	1234063918112768 = 213 · 176 · 792	Discriminant
Eigenvalues	2-  0  0  0 -2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-35605,-1948179]	[a1,a2,a3,a4,a6]
Generators	[-81:672:1]	Generators of the group modulo torsion
j	4991662883279390625/1234063918112768	j-invariant
L	4.4987651656253	L(r)(E,1)/r!
Ω	0.35383985006756	Real period
R	0.97800985058123	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	21488c2 85952d2 24174d2 67150d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2686b2

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
-	0	0	0	-2	-2	+	0	4	-6	8	2	-10	-2	-12	-12	-10	6	4	0	-6	-	8	14	-2

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Quadratic twists for elliptic curve 2686b2

-4	8	-3	5	17
21488c2	85952d2	24174d2	67150d2	45662k2

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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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