Preprint A93/2001
On Curves with many rational points over Finite Fields

Arnaldo Garcia

**Keywords: **
maximal curves | towers | Drinfeld-Vladut bound

We summarize results on curves attaining the Hasse-Weil upper bound for the number of rational points on curves over finite fields.We also present some towers of curves attaining the Drinfeld-Vladut bound for the ratios of the number of rational points over the genus.Especially interesting is the description by their coordinates of the supersingular points of the modular curves X_0(2^n),for each natural number n.