A probabilistic model for the distribution of ranks of elliptic curves over $\mathbb{Q}$

Abstract

In this article, we propose a new probabilistic model for the distribution of ranks of elliptic curves in families of fixed Selmer rank, and compare the predictions with previous results, and with the databases of curves over the rationals that we have at our disposal. In addition, we document a phenomenon we refer to as Selmer bias that seems to play an important role in the data and in our models.

This third version is a major revision of the paper after a wonderful referee report that had many suggestions and comments. I would like to express my gratitude to the anonymous referee