  The representation theory of a 3-dimensional Sklyanin algebra $S$ depends on
its (noncommutative projective algebro-) geometric data: an elliptic curve $E$
in $\mathbb{P}^2$, and an automorphism $\sigma$ of $E$ given by translation by
a point. Indeed, by a result of Artin-Tate-van den Bergh, we have that $S$ is
module-finite over its center if and only if $\sigma$ has finite order. In this
case, all irreducible representations of $S$ are finite-dimensional and of at
most dimension $|\sigma|$.
  In this work, we provide an algorithm in Maple to directly compute all
irreducible representations of $S$ associated to $\sigma$ of order 2, up to
equivalence. Using this algorithm, we compute and list these representations.
To illustrate how the algorithm developed in this paper can be applied to other
algebras, we use it to recover well-known results about irreducible
representations of the skew polynomial ring $\mathbb{C}_{-1}[x,y]$.
