  Let $k=\mathbb{C}(\!(\epsilon)\!)$ be the field of complex Laurent series. We
use Galois descent techniques to show that the simple regular representations
of the species of type $(1,\, 4)$ over $k$ are naturally parametrized by the
closed points of $\mathrm{Spec}(k[x])\dot{\cup}\{1,\,2\}$. Moreover we provide
weak normal forms for those representations. We use our representatives of the
simple regular representations to describe the canonical algebras associated to
the species of type (1, 4) over k. This suggest a model of those algebras in
the sense of the work of Geiss, Leclerc and Schr\"oer [GLS17] and [GLS20].
