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	26	Product of Tamagawa factors cp
deg	4368	Modular degree for the optimal curve
Δ	-26046762057728 = -1 · 226 · 173 · 79	Discriminant
Eigenvalues	2-  0  0  0 -2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,5355,-195091]	[a1,a2,a3,a4,a6]
Generators	[63:592:1]	Generators of the group modulo torsion
j	16985493417441375/26046762057728	j-invariant
L	4.4987651656253	L(r)(E,1)/r!
Ω	0.35383985006756	Real period
R	1.9560197011625	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	21488c1 85952d1 24174d1 67150d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2686b1

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 2686b1

-4	8	-3	5	17
21488c1	85952d1	24174d1	67150d1	45662k1

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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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