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 of our model 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.

中文翻译：

---

椭圆曲线在 Q 上的秩分布的概率模型

摘要 在本文中，我们提出了一个新的概率模型，用于固定 Selmer 秩家族中椭圆曲线的秩分布，并将我们模型的预测与以前的结果进行比较，并与我们在有理数上的曲线数据库进行比较。我们的处置。此外，我们记录了一种我们称为 Selmer 偏差的现象，它似乎在数据和我们的模型中发挥着重要作用。