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	16112a	Isogeny class
Conductor	16112	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	59360	Modular degree for the optimal curve
Δ	-357112186510448 = -1 · 24 · 19 · 537	Discriminant
Eigenvalues	2+ -1  0  4  5 -6 -5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17348,1270759]	[a1,a2,a3,a4,a6]
Generators	[27993:214717:343]	Generators of the group modulo torsion
j	-36089179133728000/22319511656903	j-invariant
L	4.396325314286	L(r)(E,1)/r!
Ω	0.49788031709018	Real period
R	8.8300845873563	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	8056a1 64448n1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 16112a1

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
+	-1	0	4	5	-6	-5	+	-6	4	3	2	6	1	8	+	-8	0	1	11	2	-4	18	-12	14

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Quadratic twists for elliptic curve 16112a1

-4	8
8056a1	64448n1

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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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