# EQUATIONS FOR MODULAR CURVES ASSOCIATED TO NORMALIZERS OF NON-SPLIT CARTAN SUBGROUPS

In this joint work with Pietro Mercuri, we describe a method to compute for a prime $p$, equations over $\mathbb{Q}$ of the modular curve associated to the normalizer of a non-split Cartan subgroup of $\operatorname{GL}_2(\mathbb{F}_p)$. For $p = 17, 19$ and $23$ we present explicit equations.