A sextic diophantine chain and a related Mordell curve
Ajai Choudhry, Arman Shamsi Zargar

TL;DR
This paper finds parametric and numerical solutions to a sextic Diophantine chain, leading to the construction of Mordell curves with rank at least 6, advancing understanding of rational points on these curves.
Contribution
It introduces new parametric solutions to a sextic Diophantine chain and constructs Mordell curves with generic rank at least 6 based on these solutions.
Findings
Constructed a family of Mordell curves with rank ≥ 6
Generated multiple rational points on Mordell curves from solutions
Provided parametric and numerical solutions to a sextic Diophantine chain
Abstract
In this paper we obtain parametric as well as numerical solutions of the sextic diophantine chain where is a sextic form defined by and is an integer. Each numerical solution of such a sextic chain yields, in general, nine rational points on the Mordell curve . While all of these nine points are not independent in the group of rational points of the Mordell curve, we have constructed a parameterized family of Mordell curves of generic rank using the aforementioned parametric solution of the sextic diophantine chain. Similarly, the numerical solutions of the sextic chain yield additional examples of Mordell curves whose rank is .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Commutative Algebra and Its Applications
