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	5577a	Isogeny class
Conductor	5577	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1296	Modular degree for the optimal curve
Δ	-93308787 = -1 · 33 · 112 · 134	Discriminant
Eigenvalues	0 3+  2  1 11+ 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,113,-102]	[a1,a2,a3,a4,a6]
Generators	[6:27:1]	Generators of the group modulo torsion
j	5537792/3267	j-invariant
L	3.1868641082383	L(r)(E,1)/r!
Ω	1.1158698617238	Real period
R	1.4279730179804	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	89232cn1 16731j1 61347a1 5577f1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 5577a1

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	+	2	1	+	+	2	-4	4	-8	-3	10	-8	-7	8	-10	8	13	11	-6	-13	-7	-6	8	-7

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Quadratic twists for elliptic curve 5577a1

-4	-3	-11	13
89232cn1	16731j1	61347a1	5577f1

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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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