AbstractWe relate the study of Landau–Siegel zeros to the ranks of Jacobians of modular curves for large primes . 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 have analytic rank . We show that either Landau–Siegel zeros do not exist, or that, for wide ranges of , almost all such newforms have analytic rank . In particular, in wide ranges, almost all odd newforms have analytic rank equal to one. Additionally, for a sparse set of primes in a wide range, we show that the rank of is asymptotically equal to the rank predicted by the Brumer–Murty conjecture.