Cremona's table of elliptic curves

6566 = 2 · 7² · 67

Field	Data	Notes
Atkin-Lehner	2- 7- 67+	Signs for the Atkin-Lehner involutions
Class	6566l	Isogeny class
Conductor	6566	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	884714816384 = 27 · 73 · 674	Discriminant
Eigenvalues	2-  2 -2 7- -4  2  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4124,-93059]	[a1,a2,a3,a4,a6]
Generators	[-43:105:1]	Generators of the group modulo torsion
j	22614768361639/2579343488	j-invariant
L	7.1543387000885	L(r)(E,1)/r!
Ω	0.60018166648418	Real period
R	1.7028983769431	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	52528bu2 59094w2 6566m2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6566l2

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	-	-4	2	4	-6	0	2	-4	2	-8	-4	-4	-6	10	-2	+	-12	8	-16	2	0	8

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Quadratic twists for elliptic curve 6566l2

-4	-3	-7
52528bu2	59094w2	6566m2

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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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