Towards strong uniformity for isogenies of prime degree

Abstract: Let $E$ be an elliptic curve over a number field $k$ of degree $d$ that admits a $k$-rational isogeny of prime degree $p$. We study the question of finding uniform bounds on $p$ that depend only $d$, and, under a certain condition on the signature of the isogeny, explicitly construct non-zero integers that $p$ must divide. As a corollary, we find a bound on prime order torsion points defined over unramified extensions of the base field. This is work in progress joint with Maarten Derickx.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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