Cremona's table of elliptic curves

5043 = 3 · 41²

Field	Data	Notes
Atkin-Lehner	3+ 41+	Signs for the Atkin-Lehner involutions
Class	5043b	Isogeny class
Conductor	5043	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-1650987095148745323 = -1 · 3 · 4111	Discriminant
Eigenvalues	-2 3+ -4  2  3  6 -3  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,33060,-61787848]	[a1,a2,a3,a4,a6]
Generators	[19546:966571:8]	Generators of the group modulo torsion
j	841232384/347568603	j-invariant
L	1.3905117158071	L(r)(E,1)/r!
Ω	0.1247854186621	Real period
R	5.5716113738116	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	80688bi2 15129e2 126075x2 123a2	Quadratic twists by: -4 -3 5 41

Hecke Eigenvalues for elliptic curve 5043b2

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	+	-4	2	3	6	-3	0	-6	-5	7	-7	+	-1	-3	6	0	-3	2	3	-11	-10	-16	10	12

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Quadratic twists for elliptic curve 5043b2

-4	-3	5	41
80688bi2	15129e2	126075x2	123a2

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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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