# Double Covers of Cartan Modular Curves

## TL;DR

This paper develops a method to explicitly compute equations for modular double covers related to split and non-split Cartan subgroups of GL_2 over finite fields, demonstrated through the level 13 case.

## Contribution

It introduces a new strategy for deriving explicit equations of modular double covers for Cartan subgroups, including both split and non-split cases.

## Key findings

- Successfully applied to level 13 case
- Provides explicit equations for the double covers
- Advances computational methods in modular curve theory

## Abstract

We present a strategy to obtain explicit equations for the modular double covers associated respectively to both a split and a non-split Cartan subgroup of $\text{GL}_2(\mathbb F_{p})$ with $p$ prime. Then we apply it successfully to the level $13$ case.