Typically bounding torsion on elliptic curves isogenous to rational $j$-invariant

Tyler Genao

Typically bounding torsion on elliptic curves isogenous to rational $j$-invariant

Number Theory 2022-10-18 v2

Authors: Tyler Genao

Abstract

We prove that the family $\mathcal{I}_{F_0}$ of elliptic curves over number fields that are geometrically isogenous to an elliptic curve with $F_0$ -rational $j$ -invariant is typically bounded in torsion. Under an additional uniformity assumption, we also prove that the family $\mathcal{I}_{d_0}$ of elliptic curves over number fields that are geometrically isogenous to an elliptic curve with degree $d_0$ $j$ -invariant is typically bounded in torsion.

Keywords

elliptic curves torsion j-invariant isogeny number fields typical boundedness

Cite

@article{arxiv.2112.11566,
  title  = {Typically bounding torsion on elliptic curves isogenous to rational $j$-invariant},
  author = {Tyler Genao},
  journal= {arXiv preprint arXiv:2112.11566},
  year   = {2022}
}

Comments

8 pages, to appear in Proceedings of the AMS

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