Mordell–Weil finite-generation conjecture over suitable real abelian fields

Let $E$ be an elliptic curve over $\mathbb{Q}$, and let $\mathbf L\subset\mathbb{Q}^{\operatorname{ab}}$ be a real abelian field containing only finitely many extensions of $\mathbb{Q}$ of degree $2$, $3$, or $5$. Mordell–Weil finite-generation conjecture. Then $E(\mathbf L)$ is finitely generated. The conjecture is presented as one of two conjectures motivated by statistics of modular symbols and earlier random-matrix heuristics; the source gives no resolution.