3 problems

Let $E$ be a non-CM elliptic curve over $\mathbb{Q}$, let $L\geq 2$ be fixed, and let $\mathcal{G}_E$ be the directed graph constructed from the trace and determinant data of the G…

Let $E/\mathbb Q$ be an elliptic curve, and let $\mathcal P_E^{[\ell]}(X)$ count tuples $(p_1,\ldots,p_\ell)$ of distinct primes with $p_1\le X$ such that … No condition is imposed…

Let $E/\mathbb{Q}$ be an elliptic curve without complex multiplication. For an integer $\ell\ge1$, let $\mathcal Q_{E,\ell}(X)$ count normalized aliquot cycles…