a crowning achievement of number theory in the 20th century is a theorem of wiles which states that for an elliptic curve $e$ over $\mathbb{q}$ of conductor $n$, there is a non-constant map from the modular curve $x_0(n)$ to $e$. for some curve isogenous to $e$, the degree of this map will be minimal; this is the modular degree. the jacquet-langlands correspondence allows us to similarly parameterize elliptic curves by shimura curves. in this case we have several different shimura curve parameterizations for a given isogeny class. further, this generalizes to elliptic curves over totally real number fields. in this talk i will discuss these degrees and i compare them with $d$-new modular degrees and $d$-new congruence primes. this data indicates that there is a strong relationship between shimura degrees and new modular degrees and congruence primes.