An elliptic curve over Q(u) with torsion Z/4Z and rank 6

TL;DR

This paper constructs an elliptic curve over the rational function field with torsion group Z/4Z and rank 6, surpassing the previously known maximum rank of 5 for such curves.

Contribution

It provides the first known example of an elliptic curve over Q(u) with torsion Z/4Z and rank 6, advancing the understanding of possible ranks in this context.

Findings

Constructed an elliptic curve over Q(u) with torsion Z/4Z and rank 6

Demonstrated that higher ranks than previously known are achievable for such curves

Contributed to the classification of elliptic curves with specific torsion and rank properties.

Abstract

In this note we present the main details of the construction of an elliptic curve over $\mathbb{Q}(u)$ with torsion $\mathbb{Z}/4\mathbb{Z}$ and rank 6. Previously only rank 5 examples for such curves were known.