  We push further the classical proof of Weil upper bound for the number of
rational points of an absolutely irreducible smooth projective curve $X$ over a
finite field in term of euclidean relationships between the Neron Severi
classes in $X\times X$ of the graphs of iterations of the Frobenius morphism.
This allows us to recover Ihara's bound, which can be seen as a {\em second
order} Weil upper bound, to establish a new {\em third order} Weil upper bound,
and using {\tt magma} to produce numerical tables for {\em higher order} Weil
upper bounds. We also give some interpretation for the defect of exact
recursive towers, and give several new bounds for points of curves in relative
situation $X \rightarrow Y$.
