Cremona's table of elliptic curves

6565 = 5 · 13 · 101

Field	Data	Notes
Atkin-Lehner	5- 13+ 101+	Signs for the Atkin-Lehner involutions
Class	6565d	Isogeny class
Conductor	6565	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	3040	Modular degree for the optimal curve
Δ	414415625 = 55 · 13 · 1012	Discriminant
Eigenvalues	-1 -2 5-  0 -2 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-880,9927]	[a1,a2,a3,a4,a6]
Generators	[9:48:1] [14:13:1]	Generators of the group modulo torsion
j	75370704203521/414415625	j-invariant
L	2.789832402548	L(r)(E,1)/r!
Ω	1.689565913765	Real period
R	0.66048501092938	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	105040v1 59085d1 32825d1 85345a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6565d1

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

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Quadratic twists for elliptic curve 6565d1

-4	-3	5	13
105040v1	59085d1	32825d1	85345a1

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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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