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We classify the possible torsion structures of rational elliptic curves overquintic number fields. In addition, let E be an elliptic curve defined over Qand let G = E(Q)_tors be the associated torsion subgroup. We study, for a givenG, which possible groups G \subseteq H could appear such that H=E(K)_tors, for[K:Q]=5. In particular, we prove that at most there is a quintic number field Ksuch that E(Q)_tors\neq E(K)_tors.

Complete classification of the torsion structures of rational elliptic curves over quintic number fields