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

Tomislav Gužvić; Borna Vukorepa

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

Number Theory 2022-07-01 v1 Algebraic Geometry

Authors: Tomislav Gužvić , Borna Vukorepa

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 $E(\mathbb{Q}(\mu_{p^{\infty}}))_{tors}$ .

Keywords

elliptic curves torsion subgroups cyclotomic extensions rational numbers prime numbers

Cite

@article{arxiv.2206.15208,
  title  = {Torsion groups of elliptic curves over $\mathbb{Q}(\mu_{p^{\infty}})$},
  author = {Tomislav Gužvić and Borna Vukorepa},
  journal= {arXiv preprint arXiv:2206.15208},
  year   = {2022}
}

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