The Maximal Rank of Elliptic Delsarte Surfaces

Details The Maximal Rank of Elliptic Delsarte Surfaces The Maximal Rank of Elliptic Delsarte Surfaces

2010-11-10

arxiv.org/abs/1011.2340v2

Mathematics

Algebraic Geometry

Scientific paper

Shioda described in his article from 1986 a method to compute the Lefschetz
number of a Delsarte surface. In one of his examples he uses this method to
compute the rank of an elliptic curve over k(t). In this article we find all
elliptic curves over k(t) for which his method is applicable. For each of these
curves we also compute the Mordell-Weil rank.

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