engleski

Counting elliptic curves with prescribed level structures over number fields

Harron and Snowden [11] counted the number of elliptic curves over Q up to height X with torsion group G for each possible torsion group G over Q. In this paper we generalize their result to all number fields and all level structures G such that the corresponding modular curve XG is a weighted projective line P(w0, w1) and the morphism XG → X(1) satisfies a certain condition. In particular, this includes all modular curves X1(m, n) with coarse moduli space of genus 0. We prove our results by defining a size function on P(w0, w1) following unpublished work of Deng [7], and working out how to count the number of points on P(w0, w1) up to size X.

elliptic curves ; torsion

nije evidentirano