Mordell-Weil Lattices in Characteristic 2, III: A Mordell-Weil Lattice of Rank 128

CONTENTS We analyze the 128-dimensional Mordell-Weil lattice of a cer1 . Introduction j -a jn elliptic curve over the rational function field k(t)f where k is 2. Statement of Results a finite field of 2 elements. By proving that the elliptic curve 3. Proof of Rank, Discriminant and Tate-Safarevic Group has trivial Tate-Safarevic group and nonzero rational points of 4. Proof of Minimal Norm, Density, and Kissing Number height 22, we show that the lattice's density achieves the lower 5 Remarks and Questions bound derived in our earlier work. This density is by a considerA , , , . able factor the largest known for a sphere packing in dimension Acknowledgements , & , , , , , , , , . 128. We also determine the kissing number of the lattice, which References is by a considerable factor the largest known for a lattice in this dimension.