Abstract
There are exactly nine reduced discriminants $D$ of indefinite quaternion algebras over $\mathbb Q$ for which the Shimura curve $X_D$ 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 ${\rm Jac}(X_0(D))^{\rm new}$ such that the abelian variety ${\rm Jac}(X_0(D))^{\rm new}/c(D)$ is the jacobian of the curve $X_D$.
Citation
Josep GONZÁLEZ. Santiago MOLINA. "The kernel of Ribet's isogeny for genus three Shimura curves." J. Math. Soc. Japan 68 (2) 609 - 635, April, 2016. https://doi.org/10.2969/jmsj/06820609
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