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	5566d	Isogeny class
Conductor	5566	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	110880	Modular degree for the optimal curve
Δ	940086052664016896 = 215 · 119 · 233	Discriminant
Eigenvalues	2-  2  3  3 11+  3 -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-245209,2751079]	[a1,a2,a3,a4,a6]
j	691510653107/398688256	j-invariant
L	7.1286794472388	L(r)(E,1)/r!
Ω	0.23762264824129	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	44528j1 50094m1 5566a1 128018o1	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 5566d1

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	3	+	3	-3	0	+	3	-5	-11	0	12	-3	6	0	12	-5	9	0	-9	-12	-12	-10

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Quadratic twists for elliptic curve 5566d1

-4	-3	-11	-23
44528j1	50094m1	5566a1	128018o1

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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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