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The theory of 4-descent on elliptic curves has been developed in the PhD theses of Siksek, Womack and Stamminger. Prompted by our use of 4-descent in the search for generators of large height on elliptic curves of rank at least 2, we explain how to cut down the number of class group and unit group calculations required, by using the group law on the 4-Selmer group.

Some improvements to 4-descent on an elliptic curve  (14 pages)          

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This paper has appeared in the proceedings of ANTS VIII. The slides for my talk at the conference are here.