Genus 2 Curves with Quaternionic Multiplication
Genus 2 Curves with Quaternionic Multiplication
Abstract We explicitly construct the canonical rational models of Shimura curves, both analytically in terms of modular forms and algebraically in terms of coefficients of genus 2 curves, in the cases of quaternion algebras of discriminant 6 and 10. This emulates the classical construction in the elliptic curve case. We …