Chapter

Algorithmic Number Theory

Volume 5011 of the series Lecture Notes in Computer Science pp 125-138

Some Improvements to 4-Descent on an Elliptic Curve

  • Tom FisherAffiliated withDPMMS, Centre for Mathematical Sciences, University of Cambridge

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Abstract

The theory of 4-descent on elliptic curves has been developed in the PhD theses of Siksek [18], Womack [21] and Stamminger [20]. 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.