STNB

STNB2023(36a edició)

Coincidences of Division Fields of an elliptic curve defined over a number field

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Zoé Yvon

Resum

Let $E/F$ an elliptic curve over a number field $F$. For a positive integer $n$, the extension $F(E[n])/F$ generated by the coordinates of the $n$-torsion points, is finite and Galois. For integers $m \ne n$, we consider when the coincidence $F(E[n])=F(E[m])$ holds. Daniels and Lozano-Robledo classified coincidence when $F = \mathbb{Q}$ and $n$ and $m$ are prime powers. In this talk, we will describe some preliminary results over a general number field $F$.

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