For each quadratyic imaginary field of class number $1$ we enumerate the ielements $\gamma\in \mathcal{O}_K$, ring of integers of $K$, of norm less than or equal to $x$. Given $\gamma$ we compute $P^+(N_{K/\mathbb{Q}}(\gamma))$, the largest prime factor of the norm. Our naive computations can be replaced by an extension of the algorithm of Bernstein (2002, Millennium Journal) to the case of imaginary quadraic fields of class number $1$. We say that an integer $n$ is $y$-friable if $P^+(n)\leq y$.
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For $d=1,2,3,7,11,19,43,67,163$ and an integer $x$ the file field<d>_<x>.txt contains the smoothness results of the field $\mathbb{Q}(\sqrt{-d})$. The first colum of row $i$ gives an integer $x_i$. The $j$th following column of row $i$ gives the number of $\gamma\in \mathcal{O}_K$ of norm less than $x_i$ which are $2^j$-friable. In particular, the sum of all but the first column of row $i$ is the number of algebraic integers of norm less than or equal to $x_i$. Figure 1 in the article was created using the script field2dat.sage.
We consider the examples $E_7\colon y^2 + x y = x^{3} - x^{2} - 2 x - 1$ and $E_{11}\colon y^2 + y = x^{3} - x^{2} - 7 x + 10 $ which have endomorphism rings included in $\mathbb{Q}(\sqrt{-7})$ and $\mathbb{Q}(\sqrt{-11})$, respectively. In folder "d=7", the file appendixB-E=0,-1,1,-7,10d=11SmoothBound=128primes=<a>_<b>.txt.inert contains on the first row the number of primes in the interval [a,b] which are inert in $\mathbb{Q}(\sqrt{-7})$. The $j$th column of the second row contains the number of primes $p$ among the ones counted in the first row for which $|E(\mathbb{F}_p)|$ is $2^j$-friable. Figure 2 was created thanks to the script distributions2dat.sage.