311 citations · 1.2k across the 55 of their papers we have counts for
4 papers · 2 filters
Mordell-Weil lattices in characteristic 2, III: A Mordell-Weil lattice of rank 128
Noam D. Elkies
In the first paper of this series, we constructed a family of lattices in dimensions 2^{n+1} for positive integers n, and proved that the associated lattice packings of spheres equ…
Explicit towers of Drinfeld modular curves
Noam D. Elkies
We give explicit equations for the simplest towers of Drinfeld modular curves over any finite field, and observe that they coincide with the asymptotically optimal towers of curves…
Shimura curve computations
Noam D. Elkies
We give some methods for computing equations for certain Shimura curves, natural maps between them, and special points on them. We then illustrate these methods by working out seve…
Rational points near curves and small nonzero |x^3-y^2| via lattice reduction
Noam D. Elkies
We give a new algorithm using linear approximation and lattice reduction to efficiently calculate all rational points of small height near a given plane curve C. For instance, when…