  In this paper we compute the gonality over Q of the modular curve X1(N) for
all N <= 40 and give upper bounds for each N <= 250. This allows us to
determine all N for which X1(N) has infinitely points of degree <= 8. We
conjecture that the modular units of Q(X1(N)) are freely generated by
f_2,...,f_{[N/2]+1} where f_k is obtained from the equation for X1(k).
