  We study the representation theoretic results of the binary cubic generic
Clifford algebra $\mathcal C$, which is an Artin-Schelter regular algebra of
global dimension five. In particular, we show that $\mathcal C$ is a PI algebra
of PI degree three and compute its point variety and discriminant ideals. As a
consequence, we give a necessary and sufficient condition on a binary cubic
form $f$ for the associated Clifford algebra $\mathcal C_f$ to be an Azumaya
algebra.
