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)≅E(K)tor×Zr. 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.