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	5565c	Isogeny class
Conductor	5565	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	23710812890625 = 32 · 58 · 74 · 532	Discriminant
Eigenvalues	-1 3+ 5- 7-  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-10735,-362788]	[a1,a2,a3,a4,a6]
j	136814581691933041/23710812890625	j-invariant
L	0.94916637117862	L(r)(E,1)/r!
Ω	0.47458318558931	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	89040cq2 16695k2 27825k2 38955j2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5565c2

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

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Quadratic twists for elliptic curve 5565c2

-4	-3	5	-7
89040cq2	16695k2	27825k2	38955j2

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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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