Type: Seminar

Distribution: World

Expiry: 3 Jun 2010

Auth: billu@daumier.maths.usyd.edu.au

Speaker: Steve Donnelly Title: The method of descent: determining the rational points on elliptic curves Time & Place: 3:05-4pm, Thursday 3 June, Carslaw 535 Abstract: I’ll begin a short series of talks outlining the theory of the descent algorithms implemented in Magma, whose purpose is to determine the group of rational points on a given elliptic curve. (For elliptic curves over Q, we have 2-descent, 4-descent and now full-fledged 8-descent; alongside this, we have 3-descent and now 6- and 12-descent. Complementary to 4- and 8-descent, we have the Cassels-Tate pairing for 2- and 4-coverings.) The first talk will describe 2-descent from an elementary point of view, so it will be accessible and will lay the foundations for the remaining talks.