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	5083a	Isogeny class
Conductor	5083	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1987453 = 13 · 172 · 232	Discriminant
Eigenvalues	1  0  2  0  0 13+ 17-  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-61,-156]	[a1,a2,a3,a4,a6]
Generators	[110:251:8]	Generators of the group modulo torsion
j	25334470953/1987453	j-invariant
L	4.9015580063343	L(r)(E,1)/r!
Ω	1.7154888337992	Real period
R	2.8572369051677	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	81328i2 45747c2 127075f2 66079c2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5083a2

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
1	0	2	0	0	+	-	2	-	10	2	-2	-4	-8	-8	6	12	-14	-10	6	-16	-8	-14	0	-18

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Quadratic twists for elliptic curve 5083a2

-4	-3	5	13	17	-23
81328i2	45747c2	127075f2	66079c2	86411a2	116909a2

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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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