An algorithm based on Ribet's isogeny computes point counts for Shimura curves, yielding 116 record curves, automorphism results for 9288 of 10609 curves, and a tetragonal classification up to 32 exceptions each.
Buzzard, Integral models of certain S himura curves , Duke Math
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Point counts, automorphisms, and gonalities of Shimura curves
An algorithm based on Ribet's isogeny computes point counts for Shimura curves, yielding 116 record curves, automorphism results for 9288 of 10609 curves, and a tetragonal classification up to 32 exceptions each.