Cremona's table of elliptic curves

8240 = 2⁴ · 5 · 103

Field	Data	Notes
Atkin-Lehner	2- 5- 103+	Signs for the Atkin-Lehner involutions
Class	8240k	Isogeny class
Conductor	8240	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-87418160 = -1 · 24 · 5 · 1033	Discriminant
Eigenvalues	2- -1 5-  4  0  2  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-185,1132]	[a1,a2,a3,a4,a6]
Generators	[8:10:1]	Generators of the group modulo torsion
j	-44001181696/5463635	j-invariant
L	4.2470579458953	L(r)(E,1)/r!
Ω	1.8569276473726	Real period
R	2.2871423945378	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	2060b2 32960l2 74160bg2 41200bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8240k2

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	-	4	0	2	0	-5	-6	3	-2	2	3	-11	-3	-3	-15	-1	-5	0	-7	1	0	0	-10

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Quadratic twists for elliptic curve 8240k2

-4	8	-3	5
2060b2	32960l2	74160bg2	41200bg2

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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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