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	8162g	Isogeny class
Conductor	8162	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	17920	Modular degree for the optimal curve
Δ	-18866895781888 = -1 · 216 · 7 · 114 · 532	Discriminant
Eigenvalues	2-  0 -2 7+ 11-  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-9916,-431233]	[a1,a2,a3,a4,a6]
j	-107818231938348177/18866895781888	j-invariant
L	1.8956306040495	L(r)(E,1)/r!
Ω	0.23695382550619	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	65296w1 73458f1 57134y1 89782p1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 8162g1

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

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Quadratic twists for elliptic curve 8162g1

-4	-3	-7	-11
65296w1	73458f1	57134y1	89782p1

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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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