On the ubiquity of trivial torsion on elliptic curves

TL;DR

This paper provides a straightforward proof that most elliptic curves over the rationals have trivial torsion, emphasizing the commonality of this property in a clear and accessible manner.

Contribution

It offers a simple, accessible proof of the prevalence of trivial torsion on elliptic curves over the rationals, clarifying a well-known fact.

Findings

Most elliptic curves over the rationals have trivial torsion

The proof is straightforward and accessible

Supports the common belief about torsion properties

Abstract

The purpose of this paper is to give a "down--to--earth" proof of the well--known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.