We prove that the elliptic surface y2 = x3 + 2(t 8 + 14t4 + 1)x + 4t2(t8 + 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 ranks 0, 1, . . . , 14, 16, 17, 18. © Canadian Mathematical Society 2007.
Elliptic K3 surfaces with geometric Mordell-Weil Rank 15
KLOOSTERMAN, REMKE NANNE
2007
Abstract
We prove that the elliptic surface y2 = x3 + 2(t 8 + 14t4 + 1)x + 4t2(t8 + 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 ranks 0, 1, . . . , 14, 16, 17, 18. © Canadian Mathematical Society 2007.
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