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	5168h	Isogeny class
Conductor	5168	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	854663168 = 213 · 172 · 192	Discriminant
Eigenvalues	2-  2  4 -4 -2 -6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-61616,-5866432]	[a1,a2,a3,a4,a6]
Generators	[3682:222870:1]	Generators of the group modulo torsion
j	6316133726112049/208658	j-invariant
L	5.6572396919573	L(r)(E,1)/r!
Ω	0.30302299954993	Real period
R	4.667335235576	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	646c2 20672x2 46512bs2 129200ck2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168h2

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	4	-4	-2	-6	+	-	0	-8	-8	-4	10	0	8	-6	0	-8	-8	12	-6	4	-8	18	2

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Quadratic twists for elliptic curve 5168h2

-4	8	-3	5	17	-19
646c2	20672x2	46512bs2	129200ck2	87856t2	98192r2

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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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