5 problems

Serre's uniformity question. Does there exist an absolute constant $c$ such that, for every elliptic curve $E/\mathbb{Q}$,

Serre's uniformity conjecture. If $(\ell,j_E)$ is not one of these exceptional pairs, then

Serre's uniformity consequence. There exists an elliptic curve $E/\mathbb{Q}$ without CM such that the image of $\overline{\rho}_{E,p}$ is contained in the normalizer of a non-spli…

Let $E$ be a non-CM elliptic curve over a number field $K$. For sufficiently large primes $\ell$, the $\ell$-adic representation is surjective; denote by $r_{E/K}$ the smallest pos…

Let $E/\mathbb{Q}$ be an elliptic curve without complex multiplication, let $\ell$ be a prime, and let … be the mod-$\ell$ Galois representation. Sutherland's conjecture. The image…