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	2856i	Isogeny class
Conductor	2856	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-639744 = -1 · 28 · 3 · 72 · 17	Discriminant
Eigenvalues	2- 3-  3 7+  5 -3 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-89,-357]	[a1,a2,a3,a4,a6]
j	-307981312/2499	j-invariant
L	3.104315175165	L(r)(E,1)/r!
Ω	0.77607879379124	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5712h1 22848j1 8568d1 71400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2856i1

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
-	-	3	+	5	-3	-	-5	5	2	8	-6	9	-1	0	4	12	-6	-16	8	-10	8	14	-8	-8

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Quadratic twists for elliptic curve 2856i1

-4	8	-3	5	-7	17
5712h1	22848j1	8568d1	71400j1	19992x1	48552ba1

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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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