Cremona's table of elliptic curves

8162 = 2 · 7 · 11 · 53

Field	Data	Notes
Atkin-Lehner	2- 7+ 11- 53-	Signs for the Atkin-Lehner involutions
Class	8162h	Isogeny class
Conductor	8162	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-29844973312 = -1 · 28 · 73 · 112 · 532	Discriminant
Eigenvalues	2-  2  0 7+ 11- -2 -2  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,582,-6073]	[a1,a2,a3,a4,a6]
j	21799474625375/29844973312	j-invariant
L	5.0102773099015	L(r)(E,1)/r!
Ω	0.62628466373768	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	65296x1 73458e1 57134ba1 89782r1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 8162h1

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
-	2	0	+	-	-2	-2	6	4	-2	10	10	0	4	0	-	0	8	12	-8	8	8	-6	-2	14

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Quadratic twists for elliptic curve 8162h1

-4	-3	-7	-11
65296x1	73458e1	57134ba1	89782r1

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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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