In number theory, a pseudoprime is called an elliptic pseudoprime for (E, P), where E is an elliptic curve defined over the field of rational numbers with complex multiplication by an order in , having equation y<sup>2</sup> = x<sup>3</sup> + ax + b with a, b integers, P being a point on E and n a natural number such that the Jacobi symbol (âÂÂd | n) = âÂÂ1, if .
The number of elliptic pseudoprimes less than X is bounded above, for large X, by