Sections on certain j=0 elliptic surfaces, by Jasbir Chahal, Matthijs Meijer and Jaap Top
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.
Jasbir Chahal, Matthijs Meijer and Jaap Top <email@example.com>