  Mazur's Theorem states that there are precisely 15 possibilities for the
torsion subgroup of an elliptic curve defined over the rational numbers. It was
previously shown by Harron and Snowden that the number of isomorphism classes
of elliptic curves of height up to $X$ that have a specific torsion subgroup
$G$ is on the order of $X^{1/{d(G)}}$, for some positive $d(G)$ depending on
$G$. We compute $d(G)$ for these groups over $\mathbb{Q}[i]$. Furthermore, in a
collection of recent papers it was proven that there are 9 more possibilities
for the torsion subgroup in the base field $\mathbb{Q}[i]$. We compute the
value of $d(G)$ for these new groups.
