Sections on certain j=0 elliptic surfaces
Number Theory
2007-05-23 v1
Abstract
Using some theory of (rational) elliptic surfaces plus elementary properties of a Mordell-Weil group regarded as module over the endomorphism ring of a (CM) elliptic curve, we present examples of such surfaces with j-invariant zero. In particular, a K3 example is given with the maximal possible rank 18, plus that many explicit independent sections on it. Several other high rank cases are discussed; for instance Shioda's example with rank 68.
Cite
@article{arxiv.math/9911274,
title = {Sections on certain j=0 elliptic surfaces},
author = {Jasbir Chahal and Matthijs Meijer and Jaap Top},
journal= {arXiv preprint arXiv:math/9911274},
year = {2007}
}