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Mazur's Theorem states that there are precisely 15 possibilities for thetorsion subgroup of an elliptic curve defined over the rational numbers. It waspreviously shown by Harron and Snowden that the number of isomorphism classesof 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 acollection of recent papers it was proven that there are 9 more possibilitiesfor the torsion subgroup in the base field $\mathbb{Q}[i]$. We compute thevalue of $d(G)$ for these new groups.

The Frequency of Elliptic Curves Over $\mathbb{Q}[i]$ with Fixed Torsion