  In this paper we consider models for genus one curves of degree n for n = 2,
3 and 4, which arise in explicit n-descent on elliptic curves. We prove
theorems on the existence of minimal models with the same invariants as the
minimal model of the Jacobian elliptic curve and provide simple algorithms for
minimising a given model, valid over general number fields. Finally, for genus
one models defined over Q, we develop a theory of reduction and again give
explicit algorithms for n = 2, 3 and 4.
