Sections on certain j=0 elliptic surfaces
Jasbir Chahal, Matthijs Meijer, Jaap Top
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.
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