Determining all $(2, 3)$-torus structures of a symmetric plane curve

Abstract

In this paper, we describe all (2, 3)-torus structures of a highly symmetric 39-cuspidal degree 12 curve. A direct computer-aided determination of these torus structures seems to be out of reach. We use various quotients by automorphisms to find torus structures. We use a height pairing argument to show that there are no further structures.