  Let E/Q be an elliptic curve, let L(E,s)=\sum a_n/n^s be the L-series of E/Q,
and let P be a point in E(Q). An integer n > 2 having at least two distinct
prime factors will be be called an elliptic pseudoprime for (E,P) if E has good
reduction at all primes dividing n and (n+1-a_n)P = 0 (mod n). Then n is an
elliptic Carmichael number for E if n is an elliptic pseudoprime for every P in
E(Z/nZ). In this note we describe two elliptic analogues of Korselt's criterion
for Carmichael numbers, and we analyze elliptic Carmichael numbers of the form
pq.
