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

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- Proc. Amer. Math. Soc.
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## 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.## References

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## Additional Information

**Tyler Genao**- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 1179563
- ORCID: 0000-0003-4242-3784
- Email: tylergenao@uga.edu
- Received by editor(s): January 1, 2022
- Received by editor(s) in revised form: June 17, 2022, and September 16, 2022
- Published electronically: February 10, 2023
- Additional Notes: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1842396. Partial support was also provided by the Research and Training Group grant DMS-1344994 funded by the National Science Foundation.
- Communicated by: Romyar T. Sharifi
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**151**(2023), 1907-1914 - MSC (2020): Primary 11G05
- DOI: https://doi.org/10.1090/proc/16298