Details

David Masser ^[a] and Umberto Zannier ^[b]

Estimating isogenies on tangent spaces

Pages: 175-182
Received: 24 April 2021
Accepted in revised form: 24 May 2021
Mathematics Subject Classification: 14K02, 11G05, 11G10.
Keywords: Isogeny bounds, elliptic curves, abelian varieties.
Authors address:
[a]: Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
[b]: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

Abstract: If two elliptic curves are isogenous, then there is an integer matrix connecting their representatives in the upper half plane. When these are normalized to lie in the standard fundamental domain, we give a best possible upper bound for the matrix entries in terms of the degree of the isogeny.

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