A search for high rank congruent number elliptic curves.
Dujella, Andrej, Janfada, Ali S., Salami, Sajad (2009)
Journal of Integer Sequences [electronic only]
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Dujella, Andrej, Janfada, Ali S., Salami, Sajad (2009)
Journal of Integer Sequences [electronic only]
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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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