Dedekind zeta functions of non-Galois torsion fields of elliptic curves

TL;DR

This paper presents an algorithm for factoring primes in number fields generated by points of odd order on elliptic curves and applies it to compute Dedekind zeta function coefficients.

Contribution

It introduces a novel algorithm for prime factorization in specific elliptic curve-generated fields and computes their Dedekind zeta functions.

Findings

Algorithm effectively determines prime factorization types.

Successfully computes Dedekind zeta function coefficients.

Enhances understanding of number fields from elliptic curves.

Abstract

We give an algorithm to determine factorization types of primes in the number fields generated by a single point of odd order on an elliptic curve. We apply this to compute coefficients of the Dedekind zeta function of the field.