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	5565f	Isogeny class
Conductor	5565	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	111847568175 = 34 · 52 · 7 · 534	Discriminant
Eigenvalues	-1 3- 5- 7+  0  6  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1460,14097]	[a1,a2,a3,a4,a6]
j	344192078341441/111847568175	j-invariant
L	1.9456677737564	L(r)(E,1)/r!
Ω	0.97283388687822	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	89040bu4 16695i3 27825b4 38955d4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5565f3

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

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Quadratic twists for elliptic curve 5565f3

-4	-3	5	-7
89040bu4	16695i3	27825b4	38955d4

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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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