Explicit sections on Kuwata's elliptic surfaces

TL;DR

This paper provides explicit generators for subgroups of finite index in the Mordell-Weil groups of various elliptic surfaces, enhancing understanding of their structure.

Contribution

It introduces explicit generators for Mordell-Weil subgroups of elliptic surfaces, a novel contribution to the explicit arithmetic of these surfaces.

Findings

Explicit generators for Mordell-Weil subgroups

Applications to families of elliptic surfaces

Enhanced understanding of surface arithmetic

Abstract

We give explicit generators for subgroups of finite index of the Mordell-Weil groups of several families of elliptic surfaces introduced by Masato Kuwata.