Number Theory Seminar

Tuesday 15 May 2007, TBA

Ranks of Elliptic Curves in Cubic Extensions.
Hershy Kisilevsky (Concordia)


     Let E be an elliptic curve defined over the rational field Q. We consider the rank of E(K) as K ranges over certain families of cubic extensions of Q. Given a quadratic field F=Q(sqrt(D)), the families we consider are all cubic fields K whose Galois closures contain F. We give various criteria which are sufficient for such a family to contain an infinitely many fields for which the rank of E(K) is greater than the rank of E(Q). The cases D=1 and D=-3 are of special interest.

Last modified on 20/1/07.

Comments/corrections to Tim Dokchitser