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	8272n	Isogeny class
Conductor	8272	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-13741181696 = -1 · 28 · 11 · 474	Discriminant
Eigenvalues	2- -1  1  2 11-  0 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,595,-1007]	[a1,a2,a3,a4,a6]
Generators	[651:4418:27]	Generators of the group modulo torsion
j	90845732864/53676491	j-invariant
L	3.9704348491946	L(r)(E,1)/r!
Ω	0.73558241945467	Real period
R	1.3494187545082	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	2068a1 33088x1 74448bb1 90992m1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8272n1

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	1	2	-	0	-2	4	-9	0	7	7	-8	6	+	-14	-3	4	5	-7	-12	10	-2	-9	17

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Quadratic twists for elliptic curve 8272n1

-4	8	-3	-11
2068a1	33088x1	74448bb1	90992m1

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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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