On the cyclic torsion of elliptic curves over cubic number fields

Let E be an elliptic curve defined over a number field K. Then its Mordell-Weil group E(K) is finitely generated: E(K) congruent to E{K)(tor) x Z(r) . In this paper, we discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. For N = 169, 143, 91, 65, 77 or 55, we show that Z/NZ is not a subgroup of E(K)(tor) for any elliptic curve E over a cubic number field K. (C) 2017 Elsevier Inc. All rights reserved.