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	8272p	Isogeny class
Conductor	8272	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-8470528 = -1 · 214 · 11 · 47	Discriminant
Eigenvalues	2-  2 -2  5 11- -3 -8  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-184,-912]	[a1,a2,a3,a4,a6]
Generators	[138:219:8]	Generators of the group modulo torsion
j	-169112377/2068	j-invariant
L	5.9507045790807	L(r)(E,1)/r!
Ω	0.64736971786745	Real period
R	4.5960634354997	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1034a1 33088bc1 74448bd1 90992s1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8272p1

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	5	-	-3	-8	4	-3	-6	1	1	-5	6	+	-11	-6	-2	-13	8	-6	-17	7	-3	-7

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Quadratic twists for elliptic curve 8272p1

-4	8	-3	-11
1034a1	33088bc1	74448bd1	90992s1

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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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