Rank of elliptic curves associated to Brahmagupta quadrilaterals

• Autorzy: Farzali Izadi , Foad Khoshnam , Arman Shamsi Zargar
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G05: Elliptic curves over global fields
• 14H52: Elliptic curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 2
• Strony: 187-192

Daty

wydano

2016

Twórcy

autor

Farzali Izadi

• Department of Mathematics, Faculty of Science, Urmia University, Urmia 165-57153, Iran

autor

Foad Khoshnam

• Department of Pure Mathematics, Faculty of Basic Science, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran

autor

Arman Shamsi Zargar

• Department of Pure Mathematics, Faculty of Basic Science, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran

Identyfikatory

DOI

10.4064/cm6556-12-2015