Numerical Investigations Related to the L-Series of Certain Elliptic Curves

Abstract

According to the theorem of Mordell, the set of rational solutions E(Q) of an elliptic curve E over the rational numbers is a finitely generated abelian group. The rank of this group is called the rank of the elliptic curve and is the basic invariant of E; it is positive if and only if the equation defining E has infinitely many rational solutions.