3 problems

Let $E$ be an elliptic curve over $\mathbb{Q}$, and let $p$ be a prime. Consider cyclic extensions $L/\mathbb{Q}$ with Galois group isomorphic to $\mathbb{Z}/p\mathbb{Z}$. David–Fe…

Let $E$ be an elliptic curve over $K=\mathbb{Q}$, and let $p$ be a prime. A $\mathbb{Z}/p\mathbb{Z}$-extension $L/K$ is a finite Galois extension with Galois group isomorphic to…

Let $F/\mathbb{Q}$ be a cyclic extension of prime degree $p$. Rank-growth conjecture. There is an elliptic curve $E$ defined over $\mathbb{Q}$ such that … The source states this as…