For every group $\{\pm1\}\subseteq \Delta\subseteq (\mathbb Z/N\mathbb
Z)^\times$, there exists an intermediate modular curve $X_\Delta(N)$. In this
paper we determine all curves $X_\Delta(N)$ with infinitely many points of
degree $4$ over $\mathbb Q$. To do that, we developed a method to compute
possible degrees of rational morphisms from $X_\Delta(N)$ to an elliptic curve.

Cet article explore les excursions dans le temps et leurs implications.

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