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	5168d	Isogeny class
Conductor	5168	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	1608777728 = 218 · 17 · 192	Discriminant
Eigenvalues	2-  0  4  2 -4  6 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2003,34450]	[a1,a2,a3,a4,a6]
j	216973458729/392768	j-invariant
L	3.0035282070493	L(r)(E,1)/r!
Ω	1.5017641035246	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	646a1 20672z1 46512bg1 129200bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168d1

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	4	2	-4	6	+	+	6	0	-6	-4	6	4	0	14	4	0	-4	-10	10	10	12	14	-10

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Quadratic twists for elliptic curve 5168d1

-4	8	-3	5	17	-19
646a1	20672z1	46512bg1	129200bv1	87856f1	98192l1

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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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