Rational isolated $j$-invariants from $X_1({\ell }^n)$ and $X_0({\ell }^n)$

Abbey Bourdon, Özlem Ejder

Let $\ell$ and $n$ be positive integers with $\ell$ prime. The modular curves $X_1({\ell }^n)$ and $X_0({\ell }^n)$ are algebraic curves over $\mathbb{Q}$ whose non-cuspidal points param…