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	8240h	Isogeny class
Conductor	8240	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	-8240 = -1 · 24 · 5 · 103	Discriminant
Eigenvalues	2- -1 5+  0  4  2  8  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1,-4]	[a1,a2,a3,a4,a6]
j	-16384/515	j-invariant
L	1.8022978621192	L(r)(E,1)/r!
Ω	1.8022978621192	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	2060a1 32960t1 74160bk1 41200bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8240h1

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	+	0	4	2	8	5	-2	-1	10	6	-5	-3	9	-9	7	-13	3	12	-9	-5	-12	0	-2

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Quadratic twists for elliptic curve 8240h1

-4	8	-3	5
2060a1	32960t1	74160bk1	41200bf1

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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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