On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree

Filip Najman

Published 2011-09-28, updated 2014-02-26Version 4

Let $p$ be a prime and $K$ a number field of degree $p$. We count the number of elliptic curves, up to $\bar{K}$-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup, or that it has an isogeny of prescribed degree.