Cremona's table of elliptic curves

5565 = 3 · 5 · 7 · 53

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 53+	Signs for the Atkin-Lehner involutions
Class	5565a	Isogeny class
Conductor	5565	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1567817015625 = 36 · 56 · 72 · 532	Discriminant
Eigenvalues	1 3+ 5+ 7+  0 -2  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-15473,731952]	[a1,a2,a3,a4,a6]
Generators	[5792:437852:1]	Generators of the group modulo torsion
j	409723754843086489/1567817015625	j-invariant
L	3.4482414351262	L(r)(E,1)/r!
Ω	0.84979309203642	Real period
R	4.0577423698079	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	89040cc2 16695o2 27825q2 38955p2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5565a2

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	+	+	+	0	-2	2	8	-8	6	4	6	-10	12	-12	+	4	10	-8	-8	-14	-8	4	6	-14

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Quadratic twists for elliptic curve 5565a2

-4	-3	5	-7
89040cc2	16695o2	27825q2	38955p2

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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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