311 citations · 1.2k across the 55 of their papers we have counts for
5 papers · 1 filter
On some points-and-lines problems and configurations
Noam D. Elkies
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
Elliptic curves with 3-adic Galois representation surjective mod 3 but not mod 9
Noam D. Elkies
Let E be an elliptic curve over Q, and rho_l: Gal(Q) --> GL_2(Z_l) its l-adic Galois representation. Serre observed that for l>3 there is no proper closed subgroup of SL_2(Z_l) tha…
Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d
Noam D. Elkies
For each of n=1,2,3 we find the minimal height h^(P) of a nontorsion point P of an elliptic curve E over C(T) of discriminant degree d=12n (equivalently, of arithmetic genus n), an…
The D_4 root system is not universally optimal
Henry Cohn, John H. Conway, Noam D. Elkies +1
We prove that the D_4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no uni…
A note on integral points on elliptic curves
Mark Watkins, Noam D. Elkies
We investigate a problem considered by Zagier and Elkies, of finding large integral points on elliptic curves. By writing down a generic polynomial solution and equating coefficien…