Cremona's table of elliptic curves

5083 = 13 · 17 · 23

Field	Data	Notes
Atkin-Lehner	13+ 17- 23-	Signs for the Atkin-Lehner involutions
Class	5083c	Isogeny class
Conductor	5083	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	-45711419 = -1 · 13 · 172 · 233	Discriminant
Eigenvalues	-2 -1 -1 -4 -3 13+ 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-86,-420]	[a1,a2,a3,a4,a6]
Generators	[35:-196:1]	Generators of the group modulo torsion
j	-71163817984/45711419	j-invariant
L	0.88299604102332	L(r)(E,1)/r!
Ω	0.76108695098073	Real period
R	0.19336293526986	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	81328j1 45747d1 127075h1 66079e1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5083c1

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	-1	-1	-4	-3	+	-	-5	-	6	4	-10	12	6	8	-10	4	-10	15	-10	4	-10	3	18	17

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Quadratic twists for elliptic curve 5083c1

-4	-3	5	13	17	-23
81328j1	45747d1	127075h1	66079e1	86411c1	116909e1

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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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