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Elliptic K3 Surfaces with Geometric Mordell–Weil Rank 15

Published online by Cambridge University Press:  20 November 2018

Remke Kloosterman
Remke Kloosterman*
Affiliation:
Institut für Algebraische Geometrie, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany e-mail: [email protected]
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Abstract

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We prove that the elliptic surface ${{y}^{2}}={{x}^{3}}+2\left( {{t}^{8}}+14{{t}^{4}}+1 \right)x+4{{t}^{2}}\left( {{t}^{8}}+6{{t}^{4}}+1 \right)$ 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, … , 14, 16, 17, 18.

Keywords

14J2714J2811G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 2 , 01 June 2007 , pp. 215 - 226
Copyright
Copyright © Canadian Mathematical Society 2007

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