Elliptic K3 Surfaces with Geometric Mordell–Weil Rank 15

Abstract

AbstractWe 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 ranks 0, 1, … , 14, 16, 17, 18.