  We relate the study of Landau-Siegel zeros to the ranks of Jacobians $J_0(q)$
of modular curves for large primes $q$. By a conjecture of Brumer-Murty, the
rank should be equal to half of the dimension. Equivalently, almost all
newforms of weight two and level $q$ have analytic rank $\leq 1$. We show that
either Landau-Siegel zeros do not exist, or that almost all such newforms have
analytic rank $\leq 2$. In particular, almost all odd newforms have analytic
rank equal to one. Additionally, for a sparse set of primes $q$ we show the
rank of $J_0(q)$ is asymptotically equal to the rank predicted by the
Brumer-Murty conjecture.
