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

Andrej Dujella, Juan Carlos Peral

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.

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

Abstract

In this note we present the main details of the construction of an elliptic curve over with torsion and rank 6. Previously only rank 5 examples for such curves were known.
Paper Structure (5 sections, 19 equations)

This paper contains 5 sections, 19 equations.

Table of Contents

  1. Introduction
  2. General equation of curves with torsion group $\mathbb{Z} / 4\mathbb{Z}$
  3. Elkies model for rank $4$
  4. A curve over $\mathbb{Q}(u)$ with torsion $\mathbb{Z} / 4\mathbb{Z}$ and rank $6$
  5. Concluding remarks