LetEbe an elliptic curve overQwith complex multiplication by an order in an imaginary quadratic field. Letψn{\psi _n}denote thenth division polynomial, and letPbe a rational point ofEof infinite order. A natural numbernis called anelliptic pseudoprimeifn|ψn+1(P)n|{\psi _{n + 1}}(P)andnis composite. LetN(x)N(x)denote the number of elliptic pseudoprimes up tox. We show thatN(x)≪x(log⁡log⁡x)7/2/(log⁡x)3/2N(x) \ll x{(\log \log x)^{7/2}}/{(\log x)^{3/2}}. More generally, ifP1,…,Pr{P_1}, \ldots ,{P_r}arerindependent rational points ofEwhich have infinite order, andΓ\Gammais the subgroup generated by them, denote byNΓ(x){N_\Gamma }(x)the number of compositen≤xn \leq xsatisfyingn|ψn+1(Pi)n|{\psi _{n + 1}}({P_i}),1≤i≤r1 \leq i \leq r. Forr≥2r \geq 2, we proveNΓ(x)≪xexp⁡(−c(log⁡x)(log⁡log⁡x)){N_\Gamma }(x) \ll x\exp ( - c\sqrt {(\log x)(\log \log x))}for some positive constantc.