Cremona's table of elliptic curves

5168 = 2⁴ · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 17- 19+	Signs for the Atkin-Lehner involutions
Class	5168j	Isogeny class
Conductor	5168	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	464936763392 = 218 · 173 · 192	Discriminant
Eigenvalues	2-  2  0 -2  0  2 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2448,-32320]	[a1,a2,a3,a4,a6]
Generators	[-22:102:1]	Generators of the group modulo torsion
j	396255588625/113509952	j-invariant
L	5.0374040158312	L(r)(E,1)/r!
Ω	0.69351698881632	Real period
R	1.2105937554678	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	646e1 20672bg1 46512v1 129200bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168j1

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	0	-2	0	2	-	+	-6	6	-8	2	0	4	-12	-6	0	-4	4	-12	-10	16	12	6	8

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Quadratic twists for elliptic curve 5168j1

-4	8	-3	5	17	-19
646e1	20672bg1	46512v1	129200bl1	87856k1	98192x1

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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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