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	6566f	Isogeny class
Conductor	6566	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	71251403141224544 = 25 · 716 · 67	Discriminant
Eigenvalues	2+  2 -2 7- -4 -2  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-543141,-153759955]	[a1,a2,a3,a4,a6]
Generators	[294531875967:-6220012803017:275894451]	Generators of the group modulo torsion
j	150617170289589193/605626933856	j-invariant
L	3.5648161238579	L(r)(E,1)/r!
Ω	0.17590425645727	Real period
R	20.265661534597	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	52528bc2 59094cc2 938b2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6566f2

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

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Quadratic twists for elliptic curve 6566f2

-4	-3	-7
52528bc2	59094cc2	938b2

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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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