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	5168a	Isogeny class
Conductor	5168	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1571072 = 28 · 17 · 192	Discriminant
Eigenvalues	2+  2 -2  0  0  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-84,320]	[a1,a2,a3,a4,a6]
Generators	[-4:24:1]	Generators of the group modulo torsion
j	259108432/6137	j-invariant
L	4.7365535565467	L(r)(E,1)/r!
Ω	2.6698879121189	Real period
R	1.7740645721669	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	2584a2 20672ba2 46512g2 129200l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168a2

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

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Quadratic twists for elliptic curve 5168a2

-4	8	-3	5	17	-19
2584a2	20672ba2	46512g2	129200l2	87856b2	98192d2

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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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