Congruent elliptic curves over some $p$-adic Lie extensions

TL;DR

This paper investigates how Iwasawa invariants of elliptic curves vary over specific $p$-adic Lie extensions, focusing on $p$-congruent curves and analyzing both classical and fine Selmer groups.

Contribution

It provides new insights into the behavior of Iwasawa invariants for $p$-congruent elliptic curves over certain $p$-adic Lie extensions.

Findings

Variation patterns of Iwasawa invariants identified

Differences between classical and fine Selmer groups analyzed

Results contribute to understanding elliptic curves in Iwasawa theory

Abstract

Let $p$ be an odd prime number. In this article, we study the variation of Iwasawa invariants among $p$-congruent elliptic curves over certain $p$-adic Lie extensions. We investigate both the classical Selmer group as well as the fine Selmer group.