On the Counting Function of Elliptic Carmichael Numbers We give an upper bound for the number elliptic Carmichael numbers $n \le x$ that have recently been introduced by J. H. Silverman in the case of an elliptic curve without complex multiplication (non CM). We also discuss several possible ways for further improvements. Keywords:elliptic Carmichael numbers, applications of sieve methodsCategories:11Y11, 11N36