Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture

Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon +2

Let $\mathcal{X}:y^2=f(x)$ be a hyperelliptic curve over $\mathbb{Q}(T)$ of genus $g\ge 1$. Assume that the jacobian of $\mathcal{X}$ over $\mathbb{Q}(T)$ has no subvariety de…