Hodge to de Rham degeneration of nodal curves

We compute the Hochschild and negative cyclic homology of the nodal curves, and we show that the (noncommutative) Hodge to de Rham spectral sequence degenerates at the second page. We also classify all the Hochschild classes that can be lifted to negative cyclic homology. In particular, the result in the nodal cubic curve case is important for computation of categorical enumerative invariants.