Let $E$ be an elliptic curve of conductor $N\cdot p$ over $\mathbb{Q}$, parametrized by a map $$X_{0}(p\cdot N)\rightarrow E$$ and let $E_{\sqrt(p)}$ a real quadratic twist of $E$, defined over $\mathbb{Q}[{\sqrt{p}}]$. Then this twist is known to be parametrized by a map $$X_{0}(N)\rightarrow E_{\sqrt(p)}$$ Can the lifting of the twist $X_{0}(p\cdot N)\rightarrow X_{0}(N)$ be described explicitly?