Positivity of constants related to elliptic curves

Let E be an elliptic curve defined over Q. It is known that the structure of the reduction E(F-P) is E(F-P) similar or equal to Z/d(p)Z circle plus Z/e(p)Z (1) with d(p)vertical bar e(p). The constant C-E,C-j = Sigma(infinity)(k=1) mu(k)/[Q(E[jk]) : Q] appears as the density of primes p with good reduction for E and d(p) = j (under the GRH in the non-CM case, unconditionally in the CM case). We give appropriate conditions for this constant to be positive when j > 1. (C) 2015 Elsevier Inc. All rights reserved.