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We give a complete description of quadratic potential and twisted potentialalgebras on 3 generators as well as cubic potential and twisted potentialalgebras on 2 generators up to graded algebra isomorphisms under the assumptionthat the ground field is algebraically closed and has characteristic differentfrom 2 or 3.  We also prove that for two generated potential algebra necessary condition offinite-dimensionality is that potential contains terms of degree three, thisanswers a question of Agata Smoktunowicz and the first named author, formulatedin [AN]. We clarify situation in case of arbitrary number of generators aswell.

Potential algebras with few generators