Mordell--Weil Lattices in Charactistic 2, III: A Mordell--Weil Lattice of Rank 128
Elkies, Noam D.
Experiment. Math., Tome 10 (2001) no. 3, p. 467-474 / Harvested from Project Euclid
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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.
Publié le : 2001-05-14
Classification:  
@article{1069786351,
     author = {Elkies, Noam D.},
     title = {Mordell--Weil Lattices in Charactistic 2, III: A Mordell--Weil Lattice of Rank 128},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 467-474},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1069786351}
}

Elkies, Noam D. Mordell--Weil Lattices in Charactistic 2, III: A Mordell--Weil Lattice of Rank 128. Experiment. Math., Tome 10 (2001) no. 3, pp.  467-474. http://gdmltest.u-ga.fr/item/1069786351/