Does every conformal structure on a torus come from one of these specific embeddings in $\mathbb R^3$?

Question

In the answers to this question: https://mathoverflow.net/questions/53999/ they say that every Riemann surface can be realized as a smooth surface embedded in $\mathbb R^3$.

Question: Does every conformal structure on the torus arise from a smooth embedding of the torus in $\mathbb R^3$ given by taking the "standard torus" and applying an invertible linear transformation of $\mathbb R^3$ to it?