Cremona's table of elliptic curves

5566 = 2 · 11² · 23

Field	Data	Notes
Atkin-Lehner	2- 11- 23+	Signs for the Atkin-Lehner involutions
Class	5566f	Isogeny class
Conductor	5566	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	1896803276456 = 23 · 117 · 233	Discriminant
Eigenvalues	2- -2  3 -5 11-  1  3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-47979,4040521]	[a1,a2,a3,a4,a6]
Generators	[120:61:1]	Generators of the group modulo torsion
j	6894801108937/1070696	j-invariant
L	4.3180304293576	L(r)(E,1)/r!
Ω	0.80491032346004	Real period
R	0.89410176171259	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	44528y2 50094bh2 506c2 128018bg2	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 5566f2

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
-	-2	3	-5	-	1	3	-2	+	-3	5	-7	6	-8	3	6	-6	-8	-7	-9	16	-17	-12	6	-10

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Quadratic twists for elliptic curve 5566f2

-4	-3	-11	-23
44528y2	50094bh2	506c2	128018bg2

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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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