Point Counting on Non-Hyperelliptic Genus 3 Curves with Automorphism Group $\mathbb{Z}/2\mathbb{Z}$ using Monsky-Washnitzer Cohomology

Yih-Dar Shieh

We describe an algorithm to compute the zeta function of any non-hyperelliptic genus 3 plane curve $C$ over a finite field with automorphism group $G=\mathbb{Z}/2\mathbb{Z}$.…