How to get an attractive model

We give a fourth-order Calabi-Yau differential operator, which seems to have been missed by earlier tabulations. We draw attention to this operator because of its clear geometric interpretation and evidence that it possesses a rank-two attractor, conjecturally giving a new example of a Calabi-Yau threefold with modularity properties analogous to those of an elliptic curve over $\mathbb{Q}$.