Double Covers of Cartan Modular Curves

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.

References in corpus (6)

• On the possible images of the mod ell representations associated to elliptic curves over Q
• Generalized explicit descent and its application to curves of genus 3
• The automorphism group of the non-split Cartan modular curve of level 11
• On the automorphisms of the non-split Cartan modular curves of prime level
• The generalized Fermat equation with exponents 2, 3, n
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Cited by in corpus (3)

• Automorphisms of Cartan modular curves of prime and composite level
• Quadratic Points on Non-Split Cartan Modular Curves
• Modular Curves with many Points over Finite Fields