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Rank of elliptic curves associated to Brahmagupta quadrilaterals

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Izadi F., Khoshnam F., Zargar A.

Colloquium Mathematicum

2016

tom 143

nr 2

187-192

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Izadi F.

1 Khoshnam F.

1 Zargar A.

1 2016

Wyniki wyszukiwania

Rank of elliptic curves associated to Brahmagupta quadrilaterals