311 citations · 1.2k across the 55 of their papers we have counts for
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math.AG2002★ 14 cited
Curves of every genus with many points, II: Asymptotically good families
Noam D. Elkies, Everett W. Howe, Andrew Kresch +3
We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a…
math.NT2002★ 2 cited
Curves D y^2 = x^3 - x of odd analytic rank
Noam D. Elkies
For nonzero rational D, which may be taken to be a squarefree integer, let E_D be the elliptic curve Dy^2=x^3-x over Q arising in the "congruent number" problem. It is known that t…