Torsion of rational elliptic curves over cubic fields

Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(mathbbQ )ₜₒᵣₛ and the torsion subgroup E(K)ₜₒᵣₛ, where K is a cubic number field. In particular, we study the number of cubic number fields K such that E(Q )ₜₒᵣₛ≠ E(K)ₜₒᵣₛ.