Sesquiterpene cyclase catalyzing the production of beta-farnesene from farnesyl diphosphate. Unable to use geranyl diphosphate as substrate. (2E,6E)-farnesyl diphosphate = (E)-beta-farnesene + diphosphate Strongly inhibited by manganese at concentration higher than 20 uM. Optimum pH is 6.5-7.5. Secondary metabolite biosynthesis; terpenoid biosynthesis. Expressed in flowers. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family.