On CM elliptic curves and the cyclotomic λ-invariants of imaginary quadratic fields

Let K be an imaginary quadratic field, and fix an odd prime p that does not divide the class number of K, and is excluded from a finite set of primes depending on K. In this paper we prove that Iwasawa's lambda-invariant for the cyclotomic Zp- extension of K is greater than 1 if and only if the number of points on a certain reduced elliptic curve is divisible by p2.(c) 2023 Elsevier Inc. All rights reserved.