Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves

Michael Cerchia, Jeremy Rouse

Let $\ell$ be a prime number and let $F$ be a number field and $E/F$ a non-CM elliptic curve with a point $\alpha \in E(F)$ of infinite order. Attached to the pair $(E,\alpha )$ is the $\ell$-…