p-Torsion in Elliptic Curves over Subfields of Q (...).
S. Kamienny (1988)
Mathematische Annalen
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Displaying similar documents to “Elliptic Curves: Diophantine Torsion Solutions and Singular j-Invariants.”
p-Torsion in Elliptic Curves over Subfields of Q (...).
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Yasutsugu Fujita (2007)
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L.J. Mordell (1967)
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J.W.S. Cassels (1953)
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Stroeker, Roel J., de Weger, Benjamin M.M. (1994)
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Rank of elliptic curves associated to Brahmagupta quadrilaterals
Farzali Izadi, Foad Khoshnam, Arman Shamsi Zargar (2016)
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We construct a family of elliptic curves with six parameters, arising from a system of Diophantine equations, whose rank is at least five. To do so, we use the Brahmagupta formula for the area of cyclic quadrilaterals (p³,q³,r³,s³) not necessarily representing genuine geometric objects. It turns out that, as parameters of the curves, the integers p,q,r,s along with the extra integers u,v satisfy u⁶+v⁶+p⁶+q⁶ = 2(r⁶+s⁶), uv = pq, which, by previous work, has infinitely many integer solutions. ...
Torsion points on elliptic curves over fileds of low degree.
S. Kamienny (1989)
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Darrin Doud (1998)
Manuscripta mathematica
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