|Date:||Mon, September 13, 2010|
|Place:||Research II Lecture Hall|
Abstract: Elliptic curves are curves whose set of points carries a natural group structure. If the curve is defined over an algebraic number field K, then its K-rational points form a finitely generated abelian group. In particular, the torsion subgroup is finite. So it is a natural question which natural numbers occur as the order of a torsion point on an elliptic curve over a number field of degree at most d. I will report on joint work with Sheldon Kamienny and William Stein; we determined the set of prime numbers that occur in this setting when d=4.