1) Function Chabauty-Coleman( $C^{\prime }$ , p, $C^{\prime }{\left(\mathbb{Q}\right)}_{\text{know}}$ ).

2) Set the p-adic precision N to $2p+4$ .

3) Set the t-adic precision M to $2p+1$ .

4) Initialize found-points := empty list.

5) for each $P\in C\left({\mathbb{F}}_p\right)$ up to the standard involution $\iota$ do.

6) Compute $f_1\mathrm{<mo>\; ;\; </mo>}{f}_2$ and $f_3$ in local coordinates.

7) for each point $Q\in C\left({\mathbb{Q}}_p\right)$ corresponding to a common zero of the $f_i$ do.

8) Add Q and $\iota \left(Q\right)$ to found-points.

9) end for.

10) end for.

11) return $\mathbb{Q}$ -points of $C^{\prime }$ .