# 3-torsion and conductor of genus 2 curves

## TL;DR

This paper presents an algorithm to compute the conductor of genus 2 curves by analyzing their Jacobian's 3-torsion over 2-adic fields, advancing computational methods in algebraic geometry.

## Contribution

The paper introduces a novel algorithm leveraging 3-torsion analysis to determine the conductor of genus 2 curves, improving computational techniques in the field.

## Key findings

- Algorithm successfully computes conductors for genus 2 curves.
- Analysis of 3-torsion over 2-adic fields is effective.
- Enhances understanding of arithmetic invariants of genus 2 curves.

## Abstract

We give an algorithm to compute the conductor for curves of genus 2. It is based on the analysis of 3-torsion of the Jacobian for genus 2 curves over 2-adic fields.