Isogenies of elliptic curves over function fields

Richard Griffon; Fabien Pazuki

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arXiv · 2005.02920

Isogenies of elliptic curves over function fields

Richard Griffon·Fabien Pazuki

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Abstract

We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the $j$-invariant in an isogeny class. The second one is an "isogeny estimate", providing an explicit bound on the degree of a minimal isogeny between two isogenous elliptic curves. We also give several corollaries of these two results.

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Richard Griffon, Fabien Pazuki. 2021-02-03. Isogenies of elliptic curves over function fields. https://arxiv.org/abs/2005.02920

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