Isomorphism classes of Doche-Icart-Kohel Curves over finite fields

TL;DR

This paper provides explicit formulas for counting the number of isomorphism classes of certain elliptic curves over finite fields, enhancing understanding of their classification within specific families.

Contribution

It introduces explicit formulas for enumerating isomorphism classes of Doche-Icart-Kohel elliptic curves over finite fields.

Findings

Derived formulas for counting isomorphism classes.

Enhanced classification of elliptic curves in the studied families.

Improved understanding of curve distribution over finite fields.

Abstract

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in two families of curves introduced by C.~Doche, T.~Icart and D.~R. Kohel.