%0 Journal Article
%T A Family of Elliptic Curves With Rank $\geq5$
%A Farzali Izadi
%A Kamran Nabardi
%J Mathematics
%D 2015
%I arXiv
%X In this paper, we construct a family of elliptic curves with rank $\geq 5$. To do this, we use the Heron formula for a triple $(A^2, B^2, C^2)$ which are not necessarily the three sides of a triangle. It turns out that as parameters of a family of elliptic curves, these three positive integers $A$, $B$, and $C$, along with the extra parameter $D$ satisfy the quartic Diophantine equation $A^4+D^4=2(B^4+D^4)$.
%U http://arxiv.org/abs/1501.03809v2