8 problems

Let $p$ be a prime satisfying … For an elliptic curve $E/\mathbb Q$, write $E(\mathbb Q(\sqrt{-p}))_{\mathrm{tors}}$ for its torsion subgroup over $\mathbb Q(\sqrt{-p})$. Existence…

Let $E$ be an elliptic curve over $\mathbb{Q}$. Its torsion subgroup $E(\mathbb{Q})_{\operatorname{tors}}$ is a finite abelian group. Levi's uniformity conjecture. There are only…

Wasserman's conjecture. The only possible torsion groups $E(K)_{tors}$ for elliptic curves $E$ over cubic number fields $K$ are the groups in the preceding two families together wi…

Let $N$ be one of the 24 integers … … For an elliptic curve $E$ over a cubic number field $K$, write $E(K)_{\operatorname{tor}}$ for its torsion subgroup. Wang's conjecture. The gr…

An elliptic curve over a number field has a Mordell–Weil rank and a torsion subgroup. The torsion groups that can occur for elliptic curves over $\mathbb{Q}$ are the groups listed…

Uniform boundedness conjecture. For every number field $K$, there exists a bound $B$ such that

Let $E$ be an elliptic curve defined over $\mathbb Q(i)$ or over $\mathbb Q(\sqrt{-3})$. The referenced theorem allows $\mathbb Z_{13}$ among the possible torsion groups over…

Let $G$ be an admissible torsion group for an elliptic curve over $\mathbb{Q}$, in the sense of Mazur's theorem, and define … Prescribed-torsion unbounded-rank conjecture. The quan…