The kernel of Ribet’s isogeny for genus three Shimura curves
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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. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD.
CitationMolina, S., Gonzalez, J. The kernel of Ribet’s isogeny for genus three Shimura curves. "Journal of the Mathematical Society of Japan", 2015.