Papers › Towards strong uniformity for isogenies of prime degree
Towards strong uniformity for isogenies of prime degree
Barinder S. Banwait, Maarten Derickx
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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 a uniform bound on p that depends only on d, and obtain, under a certain condition on the signature of the isogeny, such a uniform bound by explicitly constructing nonzero integers that p must divide. As a corollary we find a uniform bound on torsion points defined over unramified extensions of the base field, generalising Merel's Uniform Boundedness result for torsion.
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