Abstract
In this paper, we construct a family of elliptic curves with rank \(\ge 5\). 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 \(A^4+D^4=2(B^4+D^4)\).
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The authors would like to express their hearty thanks to the anonymous referee for a careful reading of the paper and for many careful comments and remarks which improved its quality.
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Izadi, F., Nabardi, K. A family of elliptic curves with rank \(\ge 5\) . Period Math Hung 71, 243–249 (2015). https://doi.org/10.1007/s10998-015-0102-3
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DOI: https://doi.org/10.1007/s10998-015-0102-3