
Let E be an elliptic curve over a number field K. Descent calculations on E can be used to find upper bounds for the rank of the MordellWeil group, and to compute covering curves that assist in the search for generators of this group. The general method of 4descent, developed in the PhD theses of Siksek, Womack and Stamminger, has been implemented in Magma (when K=Q) and works well for elliptic curves with sufficiently small discriminant. By extending work of Bremner and Cassels, we describe the improvements that can be made when E has a rational 2torsion point. In particular, when E has full rational 2torsion, we describe a method for 8descent that is practical for elliptic curves E/Q with large discriminant.