A Simple Method for High-Rank Families of Elliptic Curves with Specified Torsion

TL;DR

This paper introduces an effective and straightforward method to generate families of elliptic curves that possess high rank and share a common torsion subgroup structure, facilitating research in elliptic curve theory.

Contribution

The paper presents a novel, simple approach for constructing high-rank elliptic curve families with specified torsion subgroups, advancing methods for elliptic curve generation.

Findings

Method successfully derives high-rank elliptic families

All curves in the family share the same torsion structure

Approach simplifies previous complex constructions

Abstract

We describe a simple, but effective, method for deriving families of elliptic curves, with high rank, all of whose members have the same torsion subgroup structure.