On the isomorphism classes of Legendre elliptic curves over finite fields

TL;DR

This paper enumerates the number of isomorphism classes of Legendre elliptic curves over finite fields, providing a detailed classification relevant for cryptographic and algebraic applications.

Contribution

It introduces a method to count and classify Legendre elliptic curves over finite fields based on their isomorphism classes.

Findings

Number of isomorphism classes over finite fields determined

Explicit enumeration method provided

Results applicable to cryptography and algebraic geometry

Abstract

In this paper the number of $\mathbb{F}_q$-isomorphism classes of Legendre elliptic curves over the finite fields $\mathbb{F}_q$ is enumerated.