On the arithmetic of special values of $L$-functions for certain abelian varieties with a rational isogeny

Emmanuel Lecouturier, Jun Wang

Let $N$ and $p$ be primes $\ge 5$ such that $p\mid \mid N-1$. In this situation, Mazur defined and studied the $p$-Eisenstein quotient ${\tilde{J}}^{(p)}$ of $J_0(N)$. We prove a k…