Cremona's table of elliptic curves

8272 = 2⁴ · 11 · 47

Field	Data	Notes
Atkin-Lehner	2- 11+ 47+	Signs for the Atkin-Lehner involutions
Class	8272g	Isogeny class
Conductor	8272	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-26602927763456 = -1 · 212 · 113 · 474	Discriminant
Eigenvalues	2-  1 -3  2 11+  0 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-837,248051]	[a1,a2,a3,a4,a6]
j	-15851081728/6494855411	j-invariant
L	1.0843398208424	L(r)(E,1)/r!
Ω	0.54216991042118	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	517c1 33088be1 74448bu1 90992l1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8272g1

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	-3	2	+	0	-6	-8	5	-4	-3	3	4	6	+	2	3	8	11	3	-4	-2	14	-1	-15

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Quadratic twists for elliptic curve 8272g1

-4	8	-3	-11
517c1	33088be1	74448bu1	90992l1

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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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