Cremona's table of elliptic curves

5577 = 3 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	3+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	5577d	Isogeny class
Conductor	5577	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	1433562273 = 33 · 11 · 136	Discriminant
Eigenvalues	-1 3+  2 -4 11+ 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1102,-14422]	[a1,a2,a3,a4,a6]
Generators	[-492:335:27]	Generators of the group modulo torsion
j	30664297/297	j-invariant
L	1.964136388496	L(r)(E,1)/r!
Ω	0.82909834379939	Real period
R	4.7380058184538	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	89232co1 16731k1 61347j1 33a2	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 5577d1

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	+	2	-4	+	+	-2	0	8	-6	8	-6	2	0	-8	6	4	6	4	0	14	-4	-12	6	-2

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Quadratic twists for elliptic curve 5577d1

-4	-3	-11	13
89232co1	16731k1	61347j1	33a2

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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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