  The algebra of differential invariants under $SA_3(\mathbb{R})$ of generic
parabolic surfaces $S^2 \subset \mathbb{R}^3$ with nonvanishing Pocchiola
$4^{\text{th}}$ invariant $W$ is shown to be generated, through invariant
differentiations, by only one other invariant, $M$, of order $5$, having $57$
differential monomials. The proof is based on Fels-Olver's recurrence formulas,
pulled back to the parabolic jet bundles.
