Massey products for elliptic curves of rank 1

TL;DR

This paper develops a method using Massey products and Selmer varieties to explicitly describe integral points on elliptic curves of rank 1 within their p-adic points.

Contribution

It introduces a novel approach combining Massey products and secondary cohomology to find explicit equations for integral points on rank 1 elliptic curves.

Findings

Explicit equations for integral points derived

Method applicable to elliptic curves of rank 1

Enhanced understanding of p-adic point structures

Abstract

For an elliptic curve over Q of analytic rank 1, we use the level-two Selmer variety and secondary cohomology products to find explicit analytic defining equations for global integral points inside the set of p-adic points.