Number Theory Seminar

Tuesday 29 May 2007, MR13, 2:30

Finding rational points on elliptic curves using 6-descent and 12-descent
Tom Fisher (Cambridge)


     Descent on an elliptic curve E is used to obtain partial information about both the group of rational points (the Mordell-Weil group) and the failure of the Hasse principle for certain twists of E (the Tate-Shafarevich group). The Selmer group elements computed may be represented as n-coverings of E. Traditionally one takes n to be a prime power. Breaking with this tradition, I explain how to combine the data of an m-covering and an n-covering, for m and n coprime, to obtain an mn-covering. This technique improves the search for rational points on E. In particular using 6-descent and 12-descent, I was recently able to find all the "missing" generators for the elliptic curves of analytic rank 2 in the Stein-Watkins database.

Last modified on 17/4/2007.

Comments/corrections to Tim Dokchitser