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2001 Mordell--Weil Lattices in Charactistic 2, III: A Mordell--Weil Lattice of Rank 128
Noam D. Elkies
Experiment. Math. 10(3): 467-474 (2001).

Abstract

We analyze the $128$-dimensional Mordell--Weil lattice of a certain elliptic curve over the rational function field k(t), where k is a finite field of $2^{12}$ elements. By proving that the elliptic curve has trivial Tate--Šafarevič group and nonzero rational points of height $22$, we show that the lattice's density achieves the lower bound derived in our earlier work. This density is by a considerable factor the largest known for a sphere packing in dimension 128. We also determine the kissing number of the lattice, which is by a considerable factor the largest known for a lattice in this dimension.

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Noam D. Elkies. "Mordell--Weil Lattices in Charactistic 2, III: A Mordell--Weil Lattice of Rank 128." Experiment. Math. 10 (3) 467 - 474, 2001.

Information

Published: 2001
First available in Project Euclid: 25 November 2003

zbMATH: 1040.11041
MathSciNet: MR1917431

Rights: Copyright © 2001 A K Peters, Ltd.

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Vol.10 • No. 3 • 2001
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