In the famous proof of the Mordell conjecture by Gerd Faltings, the so-called Parshin construction is known. 

For example, let $E/\mathbb{Q}$ be an smooth elliptic curve, and let us pick up a $\mathbb{Q}$-rational point $P$ on $E$ (i.e. $x, y$ coordinates are both lying in $\mathbb{Q}$). 

According to Parshin's construction, we can associate the covering $p:C \to E$ to $P$. 

Could you please provide me with any "explicit" example of this covering $p$?