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Elliptic K3 surfaces with geometric Mordell-Weil rank 15

Remke Kloosterman
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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 rank 0,1,..., 14, 16, 17,18.

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Remke Kloosterman. 2005-02-21. Elliptic K3 surfaces with geometric Mordell-Weil rank 15. https://arxiv.org/abs/math/0502439

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