Involved in the production of (E)-beta-farnesene, an aphid alarm pheromone. Can use both farnesyl diphosphate and geranyl diphosphate as substrate, but not geranylgeranyl diphosphate. Produces mainly (E)-beta-farnesene, but also smaller amounts of (Z)-beta-farnesene and gamma-cadinene when used with farnesyl diphosphate as substrate. In the presence of geranyl diphosphate, produces limonene, terpinolene and the acyclic monoterpene myrcene along with minor amounts of gamma-terpinene, (Z)-ocimene, (E)-ocimene and sabinene. (2E,6E)-farnesyl diphosphate = (E)-beta-farnesene + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. Optimum pH is 6.75-7.25. Secondary metabolite biosynthesis; terpenoid biosynthesis. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). The protein CAH10289 described in PubMed:16083926 is inactive. Manganese improves the fidelity of the reaction and the products consist of 98% (E)-beta-farnesene and 2% (Z)-beta-farnesene. Belongs to the terpene synthase family.