On the Existence of Hyperelliptic Curves over $\mathbb{Q}(T)$ with Certain Jacobian Ranks

Lucas Chen, Joshua Im, Steven J. Miller +1

Let $y^2=f(x,T)$ be a hyperelliptic curve of genus $g\ge 1$, defined over $\mathbb{Q}(T)$. We prove the existence of infinitely many imaginary hyperelliptic curves with a fixed…