Character sums determined by low degree isogenies of elliptic curves

TL;DR

This paper investigates character sums linked to isogenies of elliptic curves over finite fields, providing congruence conditions and explicit formulas for small degree isogenies, advancing understanding of elliptic curve structures.

Contribution

It introduces a congruence condition for character sums related to arbitrary cyclic isogenies and derives explicit formulas for small degree cases, enhancing computational methods.

Findings

Established a congruence condition for character sums

Derived explicit formulas for small degree isogenies

Enhanced understanding of elliptic curve isogeny structures

Abstract

We consider character sums determined by isogenies of elliptic curves over finite fields. We prove a congruence condition for character sums attached to arbitrary cyclic isogenies, and produce explicit formulas for isogenies of small degree.