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	5168i	Isogeny class
Conductor	5168	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	116234190848 = 216 · 173 · 192	Discriminant
Eigenvalues	2- -2  2  0  4  2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1232,2452]	[a1,a2,a3,a4,a6]
Generators	[-36:38:1]	Generators of the group modulo torsion
j	50529889873/28377488	j-invariant
L	3.2318713793989	L(r)(E,1)/r!
Ω	0.90722853748644	Real period
R	1.7811781959335	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	646b1 20672w1 46512bn1 129200cj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5168i1

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

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Quadratic twists for elliptic curve 5168i1

-4	8	-3	5	17	-19
646b1	20672w1	46512bn1	129200cj1	87856s1	98192p1

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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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