Mazur's main conjecture at Eisenstein primes

Francesc Castella, Giada Grossi, Christopher Skinner

Let $E/\mathbb{Q}$ be an elliptic curve, let $p>2$ be a prime of good reduction for $E$, and assume that $E$ admits a rational $p$-isogeny with kernel ${\mathbb{F}}_p(\varphi )$. In this pa…