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Elliptic $K3$ Surfaces with Geometric Mordell--Weil Rank $15$ |
Canad. Math. Bull. 50(2007), 215-226
Published:2007-06-01
Printed: Jun 2007
Printed: Jun 2007
- Remke Kloosterman
Abstract
We prove that the elliptic surface
$y^2=x^3+2(t^8+14t^4+1)x+4t^2(t^8+6t^4+1)$ has geometric Mordell--Weil
rank $15$. This completes a list of Kuwata, who gave explicit examples
of elliptic $K3$-surfaces with geometric Mordell--Weil ranks
$0,1,\dots, 14, 16, 17, 18$.
| MSC Classifications: |
14J27 - Elliptic surfaces 14J28 - $K3$ surfaces and Enriques surfaces 11G05 - Elliptic curves over global fields [See also 14H52] |