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	6565b	Isogeny class
Conductor	6565	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-8371195625 = -1 · 54 · 13 · 1013	Discriminant
Eigenvalues	-1  1 5+  2 -4 13+ -1  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,394,3245]	[a1,a2,a3,a4,a6]
Generators	[-7:16:1]	Generators of the group modulo torsion
j	6763063792031/8371195625	j-invariant
L	2.713227246072	L(r)(E,1)/r!
Ω	0.87685866138182	Real period
R	1.5471291814557	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	105040l1 59085f1 32825c1 85345b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6565b1

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	-4	+	-1	3	-6	8	8	10	-3	10	-8	8	-6	8	8	-15	-15	-12	14	-7	16

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Quadratic twists for elliptic curve 6565b1

-4	-3	5	13
105040l1	59085f1	32825c1	85345b1

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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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