Algebraically primitive Teichmüller curves in Ω\mathcal M_g(2g-2)^{\mathrm{hyp}}

We give a complete classification of algebraically primitive Teichmüller curves in $Ω\mathcal M_g(2g-2)^{\mathrm{hyp}}$ for $g\ge5$. They are precisely the curves generated by the double regular \((2g+1)\)-gon when \(2g+1\) is prime, and by the regular \(4g\)-gon when \(g\) is a power of two.