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	5083d	Isogeny class
Conductor	5083	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-24972779 = -1 · 13 · 174 · 23	Discriminant
Eigenvalues	0  1  3  0  1 13- 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,71,-51]	[a1,a2,a3,a4,a6]
j	39027212288/24972779	j-invariant
L	2.4342531488374	L(r)(E,1)/r!
Ω	1.2171265744187	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	81328q1 45747k1 127075d1 66079a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5083d1

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	1	3	0	1	-	+	5	+	2	0	2	2	10	-4	0	12	0	-3	8	-12	10	13	6	1

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Quadratic twists for elliptic curve 5083d1

-4	-3	5	13	17	-23
81328q1	45747k1	127075d1	66079a1	86411g1	116909j1

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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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