| Résume | he $L$-function of a non-isotrivial elliptic curve over a function field is known to be a polynomial with integer coefficients. After discussing a brute-force method to compute this polynomial, we will provide optimizations that allow for the efficient computation of the $L$-function of any elliptic curve. These computations were carried out for a handful of curves to form a large database of elliptic curve $L$-functions that has been used for various investigations. Time permitting, we will discuss a pair of such investigations |
