On computing the Newton polygons of plus and minus $p$-adic $L$-functions

Abstract

Let $p\geq3$ be a prime number and $E/\mathbb{Q}$ an elliptic curved with good supersingular reduction at $p$ and $a_p(E)=0$. In this article, we study the computation of the Newton polygons of Pollack's plus and minus $p$-adic $L$-functions attached to $E$. In particular, we furnish new examples where the assumption GCD in [Forum Math. Sigma, 7:Paper No. e25] holds. We also take this opportunity to rectify two imprecisions in the aforementioned article.