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Counting elliptic curves with an N-rational isogeny

Soumya Sankar, University of Wisconsin, Madison
Tuesday, January 28, 2020 - 11:00am to 11:50am
PDL C-401

Counting rational elliptic curves with a rational N-isogeny is a classical problem that can be rephrased as counting points on the modular curve X_0(N). A lot of classical work in this direction tends to brush the stacky nature of X_0(N) under the rug. I will talk about how one counts points on these stacks, specifically for certain  modular curves of genus 0.  I will also talk about how this fits into the context of the recent theory of heights on stacks developed by Ellenberg, Satriano and Zureick-Brown. In particular, I will show that counting elliptic curves via the classical, naive height agrees with the count obtained from the stacky height. 

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