Cremona's table of elliptic curves

5289 = 3 · 41 · 43

Field	Data	Notes
Atkin-Lehner	3+ 41+ 43+	Signs for the Atkin-Lehner involutions
Class	5289b	Isogeny class
Conductor	5289	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	339360	Modular degree for the optimal curve
Δ	-9.1433408722856E+20	Discriminant
Eigenvalues	0 3+ -2  5  2 -4  4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-4890559,-4408069026]	[a1,a2,a3,a4,a6]
Generators	[28380915661759474:18258716683351056460:68568592357]	Generators of the group modulo torsion
j	-12935979206760765676552192/914334087228562729683	j-invariant
L	2.712186561678	L(r)(E,1)/r!
Ω	0.050555149664792	Real period
R	26.824038497178	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	84624x1 15867e1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 5289b1

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	5	2	-4	4	-5	-8	7	-5	8	+	+	-8	10	-9	6	-8	0	-2	-2	1	3	4

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Quadratic twists for elliptic curve 5289b1

-4	-3
84624x1	15867e1

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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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