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	2	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	186412613625 = 33 · 53 · 7 · 534	Discriminant
Eigenvalues	1 3+ 5+ 7+  0 -2  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1428,-1197]	[a1,a2,a3,a4,a6]
Generators	[-18488:45137:512]	Generators of the group modulo torsion
j	322391399464009/186412613625	j-invariant
L	3.4482414351262	L(r)(E,1)/r!
Ω	0.84979309203642	Real period
R	8.1154847396157	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	89040cc1 16695o1 27825q1 38955p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5565a1

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 5565a1

-4	-3	5	-7
89040cc1	16695o1	27825q1	38955p1

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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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