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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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. ...
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