Rational Elliptic Surface Related to the Question of Expressing Squares as Sum ofConsecutive Squares

摘要

The theory of Mordell-Weil lattices is applied to a specific example of arational elliptic surface. This provides a complete description of the sections of this surface, and of the sections which are defined over Q. The surface is related to the diophantine problem of expressing squares as a sum of consecutive squares. Some consequences which the description has to this problem are discussed.