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

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

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

Could you please provide me with any ``explicit’’ example of this covering p?

Sincerely yours, Pierre MATSUMI

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 $p$?