Number of general Jacobi quartic curves over finite fields

TL;DR

This paper counts the distinct isomorphism classes of general Jacobi quartic curves over finite fields, focusing on their classification via $j$-invariants.

Contribution

It provides a precise enumeration of the number of isomorphism classes of general Jacobi quartic curves over finite fields.

Findings

Number of isomorphism classes over finite fields is determined.

Enumeration based on distinct $j$-invariants.

Results contribute to understanding the classification of these curves.

Abstract

In this paper the number of $\bar{\mathbb{F}}_q$-isomorphism classes of general Jacobi quartic curves, i.e., the number of general Jacobi quartic curves with distinct $j$-invariants, over the finite field $\mathbb{F}_q$ is enumerated.