3 problems

Let $E/\mathbb Q$ be an elliptic curve, let $p$ be a prime, and let $G\subseteq \operatorname{GL}(2,\mathbb Z/p\mathbb Z)$ be the image of the mod-$p$ Galois representation…

The no-large-prime coincidence conjecture. If $p\geq 5$, then there are no non-CM elliptic curves $\mathcal{E}$ over $\mathbb{Q}$ with a $p$-coincidence. This is a more focused for…

Let $\mathcal{E}$ be a non-CM elliptic curve over $\mathbb{Q}$, let $j$ be a positive integer, and let $\mathcal{C}_{\mathcal{E},j}$ denote the constant considered in the paper. A…