Geodesic
Rank of elliptic curves associated to Brahmagupta quadrilaterals
Farzali Izadi 1   ; Foad Khoshnam 2   ; Arman Shamsi Zargar 2
1 Department of Mathematics Faculty of Science Urmia University Urmia 165-57153, Iran
2 Department of Pure Mathematics Faculty of Basic Science Azarbaijan Shahid Madani University Tabriz 53751-71379, Iran
Colloquium Mathematicum, Tome 143 (2016) no. 2, pp. 187-192 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $(p^3,q^3,r^3,s^3)$ 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 $u^6+v^6+p^6+q^6=2(r^6+s^6)$, $uv=pq$, which, by previous work, has infinitely many integer solutions.
DOI : 10.4064/cm6556-12-2015
Keywords: construct family elliptic curves six parameters arising system diophantine equations whose rank least five brahmagupta formula area cyclic quadrilaterals necessarily representing genuine geometric objects turns out parameters curves integers s along extra integers satisfy which previous work has infinitely many integer solutions

Farzali Izadi  1   ; Foad Khoshnam  2   ; Arman Shamsi Zargar  2

1 Department of Mathematics Faculty of Science Urmia University Urmia 165-57153, Iran
2 Department of Pure Mathematics Faculty of Basic Science Azarbaijan Shahid Madani University Tabriz 53751-71379, Iran 
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     title = {Rank of elliptic curves associated to {Brahmagupta} quadrilaterals},
     journal = {Colloquium Mathematicum},
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Farzali Izadi; Foad Khoshnam; Arman Shamsi Zargar. Rank of elliptic curves associated to Brahmagupta quadrilaterals. Colloquium Mathematicum, Tome 143 (2016) no. 2, pp. 187-192. doi: 10.4064/cm6556-12-2015

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