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arXiv · 2302.09594

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

Matt Stokes
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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 $p^2$.

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Matt Stokes. 2023-02-19. On CM elliptic curves and the cyclotomic $\lambda$-invariants of imaginary quadratic fields. https://arxiv.org/abs/2302.09594

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