The hyperelliptic locus $V_{hyp}$ in $Q \subset \mathbb{P}^{11}$ is is birational to a product of a Hirzebruch surface $F$ with 3 copies of $\mathbb{P}^{1}$. The procedure returns a ring map corresponding to the rational map $$ \phi: F \ \times \ \mathbb{P}^1 \ \times \ \mathbb{P}^1 \ \times \ \mathbb{P}^1 \ \rightarrow \ V_{hyp} \ \subset \ \mathbb{P}^{11}.$$
The object precomputedHyperellipticPoint is a method function.