Work

Computing the Iwasawa $μ$-Invariants for Elliptic Curves over $\mathbb{Z}_2$-Extensions

Year: 2026

Type: preprint

Abstract: Let $E$ be an elliptic curve defined over rational numbers. Further assume $E$ has good ordinary reduction at $p=2$ and $E[4]$ is reducible as a $G_\mathbb{Q}$-representation. In this paper, we offer sufficient and necessary computational criteria for the algebraic Iwasawa $μ$-invariant over the cyclotomic $\mathbb{Z}_2$-extension of rational number to be $0$, $1$ or $\geq 2$. We also show that elliptic curves with isomorphic mod-$4$ representations have algebraic $μ$-invariant equal to $0$ if one of the curves does.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.31532

Authors: Lin, Zichao, Yin, Mulun

Institutions: University of Massachusetts Amherst, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: University of North Texas

OpenAlex ID: W7214622366

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