Curves of genus 2 with sqrt2 multiplication

Abstract

In this paper, we give a universal family of curves of genus 2 whose jacobians have $\sqrt{2}$ multiplication fixed by the Rosati involution, and several results based on it, including isogenies between jacobians of curves, and jacobians of curves with quaternionic multiplication.

Cited by in corpus (3)

• Counting Points on Genus 2 Curves with Real Multiplication
• Explicit $7$-torsion in the Tate-Shafarevich groups of genus $2$ Jacobians
• The Mordell-Weil rank of the Jacobian of a curve of genus 2 with multiplication by a square root of 2