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

Genao, Tyler

doi:10.1090/proc/16298

Typically bounding torsion on elliptic curves isogenous to rational $j$-invariant
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Proc. Amer. Math. Soc. 151 (2023), 1907-1914 Request permission

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.

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