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	8162k	Isogeny class
Conductor	8162	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	278722593357824 = 216 · 72 · 11 · 534	Discriminant
Eigenvalues	2- -2 -2 7- 11+  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3844369,2900933289]	[a1,a2,a3,a4,a6]
Generators	[1130:-453:1]	Generators of the group modulo torsion
j	6283460927535303731070097/278722593357824	j-invariant
L	3.8846882027411	L(r)(E,1)/r!
Ω	0.40906888239855	Real period
R	0.59352598820942	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	65296o2 73458q2 57134r2 89782e2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 8162k2

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

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Quadratic twists for elliptic curve 8162k2

-4	-3	-7	-11
65296o2	73458q2	57134r2	89782e2

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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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