Cremona's table of elliptic curves

5192 = 2³ · 11 · 59

Field	Data	Notes
Atkin-Lehner	2- 11- 59+	Signs for the Atkin-Lehner involutions
Class	5192b	Isogeny class
Conductor	5192	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-114224 = -1 · 24 · 112 · 59	Discriminant
Eigenvalues	2- -1  3 -1 11- -4 -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1,16]	[a1,a2,a3,a4,a6]
Generators	[5:11:1]	Generators of the group modulo torsion
j	2048/7139	j-invariant
L	3.6394930774826	L(r)(E,1)/r!
Ω	2.6146979650185	Real period
R	0.34798408135229	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	10384a1 41536c1 46728e1 129800h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5192b1

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	3	-1	-	-4	-2	5	-6	7	-2	4	9	-6	-4	-1	+	8	-2	-8	-12	-15	-2	-16	6

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Quadratic twists for elliptic curve 5192b1

-4	8	-3	5	-11
10384a1	41536c1	46728e1	129800h1	57112a1

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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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