Cremona's table of elliptic curves

16112 = 2⁴ · 19 · 53

Field	Data	Notes
Atkin-Lehner	2- 19+ 53-	Signs for the Atkin-Lehner involutions
Class	16112f	Isogeny class
Conductor	16112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3168	Modular degree for the optimal curve
Δ	-8249344 = -1 · 213 · 19 · 53	Discriminant
Eigenvalues	2- -2  2  1  2  3  5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-192,-1100]	[a1,a2,a3,a4,a6]
Generators	[18:40:1]	Generators of the group modulo torsion
j	-192100033/2014	j-invariant
L	4.3870930918215	L(r)(E,1)/r!
Ω	0.64059644291604	Real period
R	1.7121126492098	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2014c1 64448l1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 16112f1

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	1	2	3	5	+	-4	-5	-3	5	2	-2	3	-	-5	-15	-8	-3	6	-8	7	-6	-2

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Quadratic twists for elliptic curve 16112f1

-4	8
2014c1	64448l1

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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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