On Mordell-Weil groups of elliptic curves induced by Diophantine triples

TL;DR

This paper investigates the structure of rational point groups on specific elliptic curves derived from Diophantine triples, revealing new insights into their algebraic properties.

Contribution

It introduces a detailed analysis of elliptic curves associated with Diophantine triples, focusing on their Mordell-Weil groups and structural possibilities.

Findings

Characterization of Mordell-Weil group structures

Conditions for rational points on these elliptic curves

Examples illustrating the possible group configurations

Abstract

We study the possible structure of the groups of rational points on elliptic curves of the form y^2=(ax+1)(bx+1)(cx+1), where a,b,c are non-zero rationals such that the product of any two of them is one less than a square.