Abstract
Let [Formula: see text] be a complex number, and a class of non-semisimple and non-solvable rank two Lie conformal algebras [Formula: see text] are introduced. In this paper, conformal derivations, conformal quasiderivations, generalized conformal derivations and conformal biderivations of [Formula: see text] are studied. Besides, central extensions and conformal modules of rank one of [Formula: see text] are determined.
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