Let E be an elliptic curve over ℚ with square-free conductor N and let f ∈ S₂(N) be the associated modular form. Then via Jaquet-Langlands there is exists f′∈ S₂^D(M), where B is the quaternion algebra over ℚ of discriminant D, N = DM, and S₂^D(M) represents the quaternionic modular forms on B of level M. Takahashi shows that there is an elliptic curve E′, isogenous to E such that E′ is parameterized by the Jacobian of the Shimura curve X₀^D(M). Note that if D = 1 then this is just the modular curve case where X₀^D(N) = X₀(N). I outline an algorithm which computes the degree of this parametrization and the isogenous curve E′ and look at ways to expand this result to abelian varieties and elliptic curves over number fields.