Elliptic K3 surfaces with geometric Mordell-Weil rank 15
Abstract
We prove that the elliptic surface y2=x3+2(t8+14t4+1)x+4t2(t8+6t4+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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