Torsion subgroups of rational elliptic curves over the compositum of all cubic fields

@article{Daniels2015TorsionSO,
  title={Torsion subgroups of rational elliptic curves over the compositum of all cubic fields},
  author={Harris B. Daniels and {\'A}lvaro Lozano-Robledo and Filip Najman and Andrew V. Sutherland},
  journal={Math. Comput.},
  year={2015},
  volume={87},
  pages={425-458}
}
Let $E/\mathbb{Q}$ be an elliptic curve and let $\mathbb{Q}(3^\infty)$ be the compositum of all cubic extensions of $\mathbb{Q}$. In this article we show that the torsion subgroup of $E(\mathbb{Q}(3^\infty))$ is finite and determine 20 possibilities for its structure, along with a complete description of the $\overline{\mathbb{Q}}$-isomorphism classes of elliptic curves that fall into each case. We provide rational parameterizations for each of the 16 torsion structures that occur for… 
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