Geodesic
Elliptic K3 Surfaces with Geometric Mordell–Weil Rank 15
Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 215-226

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DOI

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.
DOI : 10.4153/CMB-2007-023-2
Mots-clés : 14J27, 14J28, 11G05 
Kloosterman, Remke. Elliptic K3 Surfaces with Geometric Mordell–Weil Rank 15. Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 215-226. doi: 10.4153/CMB-2007-023-2
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     author = {Kloosterman, Remke},
     title = {Elliptic {K3} {Surfaces} with {Geometric} {Mordell{\textendash}Weil} {Rank} 15},
     journal = {Canadian mathematical bulletin},
     pages = {215--226},
     year = {2007},
     volume = {50},
     number = {2},
     doi = {10.4153/CMB-2007-023-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-023-2/}
}
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