Cremona's table of elliptic curves

2840 = 2³ · 5 · 71

Field	Data	Notes
Atkin-Lehner	2+ 5- 71+	Signs for the Atkin-Lehner involutions
Class	2840b	Isogeny class
Conductor	2840	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	286328800000000 = 211 · 58 · 713	Discriminant
Eigenvalues	2+  3 5- -1 -2  1  2  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16867,219326]	[a1,a2,a3,a4,a6]
j	259123794463602/139808984375	j-invariant
L	3.8287348676819	L(r)(E,1)/r!
Ω	0.47859185846023	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	5680e1 22720e1 25560e1 14200d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2840b1

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	-	-1	-2	1	2	1	7	-2	1	6	-6	1	13	-6	2	10	2	+	-9	-6	-4	9	10

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Quadratic twists for elliptic curve 2840b1

-4	8	-3	5
5680e1	22720e1	25560e1	14200d1

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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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