A Family of Elliptic Curves With Rank $\geq5$
Farzali Izadi, Kamran Nabardi

TL;DR
This paper constructs a family of elliptic curves with rank at least 5 using a novel approach involving Heron’s formula and a specific quartic Diophantine equation, expanding understanding of elliptic curve ranks.
Contribution
It introduces a new method to generate elliptic curves with high rank by linking Heron’s formula to solutions of a quartic Diophantine equation.
Findings
Constructed explicit family of elliptic curves with rank ≥ 5
Established connection between Heron formula and elliptic curve parameters
Solved a specific quartic Diophantine equation related to curve construction
Abstract
In this paper, we construct a family of elliptic curves with rank . To do this, we use the Heron formula for a triple 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 , , and , along with the extra parameter satisfy the quartic Diophantine equation .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Cryptography and Residue Arithmetic
