On Some Diophantine Parameters of the Cyclic Torsion Subgroups of Odd Order of Elliptic Curves over $\mathbb{Q}$

TL;DR

This paper investigates specific Diophantine parameters associated with cyclic torsion subgroups of odd order on elliptic curves over the rational numbers, providing explicit characterizations.

Contribution

It introduces explicit Diophantine parameters for cyclic torsion subgroups of odd order on elliptic curves over ield, advancing understanding of their structure.

Findings

Explicit Diophantine parameters identified for these torsion subgroups

Characterizations enhance classification of elliptic curve torsion structures

Results applicable to rational points and elliptic curve theory

Abstract

In this paper, we give some explicit Diophantine parameters of the cyclic torsion subgroups of odd order of elliptic curves over $\mathbb{Q}$.