Torsion groups of elliptic curves over $\mathbb{Q}(μ_{p^{\infty}})$

Published 30 Jun 2022 in math.NT and math.AG | (2206.15208v1)

Abstract: Let $E/\mathbb{Q}$ be an elliptic curve and $p \in {5,7,11 }$ be a prime. We determine the possibilities for $E(\mathbb{Q}(\zeta_{p})){tors}$. Additionally, we determine all the possibilities for $E(\mathbb{Q}(\zeta{16})){tors}$ and $E(\mathbb{Q}(\zeta{27})){tors}$. Using these results we are able to determine the possibilities for $E(\mathbb{Q}(\mu{p^{{\infty}}))_{tors}$.}