On CM elliptic curves and the cyclotomic $\lambda$-invariants of imaginary quadratic fields

Matt Stokes

On CM elliptic curves and the cyclotomic $\lambda$-invariants of imaginary quadratic fields

Number Theory 2023-08-21 v2

Authors: Matt Stokes

Abstract

Let $K$ be an imaginary quadratic field, and fix a prime $p > 3$ that does not divide the class number of $K$ . In this paper we prove that Iwasawa's $\lambda$ -invariant for the cyclotomic $\mathbb{Z}_p$ -extension of $K$ is greater than $1$ if and only if the number of points on a certain reduced elliptic curve is divisible by $p^2$ .

Keywords

CM elliptic curves cyclotomic extension Iwasawa lambda-invariant imaginary quadratic fields class number reduced elliptic curve

Cite

@article{arxiv.2302.09594,
  title  = {On CM elliptic curves and the cyclotomic $\lambda$-invariants of imaginary quadratic fields},
  author = {Matt Stokes},
  journal= {arXiv preprint arXiv:2302.09594},
  year   = {2023}
}

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