Analytic ranks of automorphic L-functions and Landau-Siegel zeros

We relate the study of Landau-Siegel zeros to the ranks of Jacobians .10(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 1. We show that either Landau-Siegel zeros do not exist, or that, for wide ranges of q, almost all such newforms have analytic rank 2. In particular, in wide ranges, almost all odd newforms have analytic rank equal to one. Additionally, for a sparse set of primes q in a wide range, we show that the rank of .10(q) is asymptotically equal to the rank predicted by the Brumer-Murty conjecture.