Counting elliptic curves with a rational $N$-isogeny for small $N$

Brandon Boggess, Soumya Sankar

We count the number of rational elliptic curves of bounded naive height that have a rational $N$-isogeny, for $N\in \{2,3,4,5,6,8,9,12,16,18\}$. For some $N$, this is done by gene…