2016 Volume 68 Issue 2 Pages 609-635
There are exactly nine reduced discriminants D of indefinite quaternion algebras over ℚ for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves and, moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of Jac(X0(D))new such that the abelian variety Jac(X0(D))new/c(D) is the jacobian of the curve XD.
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