In this paper we generalize certain results concerning quantum affine algebra $U_{ q}(\hat{ sl_{ 2}})$ at the critical level to the corresponding elliptic case $E_{ q,p}(\hat{ sl_2})$. Using the Wakimoto realization of the algebra $E_{ q,p}(\hat{ sl_2})$, we construct the central elements of it at the critical level. It turns out that the so called Drinfeld conjecture originally proposed for Kac-Moody algebras also holds for the elliptic quantum algebras.
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