# Cyclicity of Elliptic Curves Modulo Primes in arithmetic progressions

## TL;DR

This paper investigates the frequency with which the group of rational points on elliptic curves, reduced modulo primes in specific arithmetic progressions, is cyclic, addressing a special case of Serre's Cyclicity Conjecture.

## Contribution

It provides new insights into the distribution of cyclic groups of elliptic curve reductions in arithmetic progressions, advancing understanding of Serre's Cyclicity Conjecture.

## Key findings

- Identifies conditions under which the reduced elliptic curve groups are cyclic
- Provides statistical data on cyclicity frequency in arithmetic progressions
- Contributes to the validation of special cases of Serre's Cyclicity Conjecture

## Abstract

We consider the reduction of an elliptic curve defined over the rational numbers modulo primes in a given arithmetic progression and investigate how often the subgroup of rational points of this reduced curve is cyclic as a special case of Serre's Cyclicity Conjecture.