  We obtain the first complete classification result for algebraically
primitive Teichm\"{u}ller curves in a stratum component in genus greater than
2. Specifically, we show that the Veech 14-gon generates the unique
algebraically primitive Teichm\"{u}ller curve in the hyperelliptic component of
the stratum $\Omega\mathcal{M}_3(2,2)$.
