In this paper, the automorphism groups of the seven classes of the so- called hyperelliptic surfaces are calculated. Writing these as (E×F)/G, where E and F are elliptic curves and G is a finite group of translations of E acting on F not only as translations, covering space theory is then used to calculate the automorphisms. Letting M be the centralizer of G in Aut(E)×Aut(F), it is then noted that in all cases M is generated by its E-translations, its F-translations, its E- automorphisms, and its F-automorphisms. Finally, two tables list the automorphism groups and generators for each.
Bennett, C.; Miranda, R. The automorphism groups of the hyperelliptic surfaces. Rocky Mountain J. Math. 20 (1990), no. 1, 31--37. doi:10.1216/rmjm/1181073156.