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	4	Product of Tamagawa factors cp
Δ	16238600192 = 213 · 172 · 193	Discriminant
Eigenvalues	2-  2  0 -2  0  2 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1170608,487880000]	[a1,a2,a3,a4,a6]
Generators	[1422850:2165970:2197]	Generators of the group modulo torsion
j	43311038625059640625/3964502	j-invariant
L	5.0374040158312	L(r)(E,1)/r!
Ω	0.69351698881632	Real period
R	7.2635625328068	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	646e4 20672bg4 46512v4 129200bl4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168j4

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 5168j4

-4	8	-3	5	17	-19
646e4	20672bg4	46512v4	129200bl4	87856k4	98192x4

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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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