On the torsion of rational elliptic curves over sextic fields

Given an elliptic curve E/\mathbb{Q} with torsion subgroup G = E(\mathbb{Q})_{\rm {tors}} we study what groups (up to isomorphism) can occur as the torsion subgroup of E base-extended to K, a degree 6 extension of \mathbb{Q}. We also determine which groups H = E(K)_{\rm {tors}} can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth over sextic fields.