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	5566c	Isogeny class
Conductor	5566	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	3585639464 = 23 · 117 · 23	Discriminant
Eigenvalues	2+  0 -3  3 11-  1  1  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-446,2316]	[a1,a2,a3,a4,a6]
Generators	[-19:70:1]	Generators of the group modulo torsion
j	5545233/2024	j-invariant
L	2.4671013625706	L(r)(E,1)/r!
Ω	1.2849375083257	Real period
R	0.48000415323414	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	44528n1 50094cb1 506e1 128018e1	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 5566c1

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
+	0	-3	3	-	1	1	2	-	-3	-5	3	-4	2	5	-14	0	6	9	5	8	11	-2	-4	-8

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Quadratic twists for elliptic curve 5566c1

-4	-3	-11	-23
44528n1	50094cb1	506e1	128018e1

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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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