Cremona's table of elliptic curves

2856 = 2³ · 3 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	2856b	Isogeny class
Conductor	2856	Conductor
∏ cp	264	Product of Tamagawa factors cp
deg	4224	Modular degree for the optimal curve
Δ	-10917334358784 = -1 · 28 · 311 · 72 · 173	Discriminant
Eigenvalues	2+ 3- -1 7+ -3  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,679,159051]	[a1,a2,a3,a4,a6]
Generators	[67:-714:1]	Generators of the group modulo torsion
j	135037162496/42645837339	j-invariant
L	3.5855883049896	L(r)(E,1)/r!
Ω	0.55798997939798	Real period
R	0.024340533672647	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	5712f1 22848e1 8568i1 71400cp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2856b1

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	1	-	-1	5	-6	4	-10	5	-9	4	0	-8	-10	0	-8	-10	-4	-2	0	-8

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Quadratic twists for elliptic curve 2856b1

-4	8	-3	5	-7	17
5712f1	22848e1	8568i1	71400cp1	19992b1	48552h1

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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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