The talk is based on my joint work with Robert Fisette. We consider the A-infinity algebra associated with a certain generator of the derived category of coherent sheaves on a smooth projective curve. In the case of an elliptic curve this A-infinity algebra can be computed explicitly, and in particular, one can recover the j-invariant by looking at the higher products m_6 and m_8. In the higher genus curve we prove that the A-infinity structure can be uniquely recovered up to homotopy from the higher products up to m_6. We also study the map from the moduli space of curves with marked points given by the products m_3.