An Example: Computing $\mathcal{E}_2((37a,5))$

This section was written by Jennifer Balakrishnan.

We consider the algorithm of Kedlaya [Ked01] in the case of elliptic curves, as illustrated with an explicit example. In so doing, we compute the matrix of absolute Frobenius for the elliptic curve $37A$ at $p = 5$ , a quantity essential to the computation of its $5$ -adic cyclotomic height pairing [MST06].