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	8	Product of Tamagawa factors cp
Δ	13103595143168 = 214 · 17 · 196	Discriminant
Eigenvalues	2-  2  0 -2  0  2 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-73168,7640256]	[a1,a2,a3,a4,a6]
Generators	[138:390:1]	Generators of the group modulo torsion
j	10576287595212625/3199119908	j-invariant
L	5.0374040158312	L(r)(E,1)/r!
Ω	0.69351698881632	Real period
R	3.6317812664034	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	646e3 20672bg3 46512v3 129200bl3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168j3

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 5168j3

-4	8	-3	5	17	-19
646e3	20672bg3	46512v3	129200bl3	87856k3	98192x3

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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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