Simple description of a Grothendieck topology on the opposite of f.p. complex algebras

Question

Let ${\cal A}$ be the category of finitely presented $\mathbb{C}$-algebras. Let $J$ be the largest subcanonical Grothendieck topology on ${{\cal A}^{op}}$ such that the local algebras in $\cal A$ are cocovered only by the maximal sieve. Is there a more explicit description of $J$? (Something analogous to the usual description of the Zariski topology in terms of a finitary basis.) Note: it contains the Zariski topology.