Moduli of parabolic bundles on an elliptic curve

A lot is known about the moduli space of parabolic bundles over curves of genus $g\ge 2$, but the lower genus cases are notably different. The goal of this article is to study the geometry of the moduli space of semistable parabolic bundles of rank $3$ with trivial determinant and one marked point on an elliptic curve. We show that this moduli space is rational, give an explicit description of its geometry, its group of automorphisms and also prove a Torelli-type result.