Counting elliptic curves over $\mathbb{Q}$ with bounded naive height

Adrian Barquero-Sanchez, Daniel Mora-Mora

In this paper, we give exact and asymptotic formulas for counting elliptic curves $E_{A,B}:y^2=x^3+Ax+B$ with $A,B\in \mathbb{Z}$, ordered by naive height. We st…