On equations of double planes with $p_g=q=1$

This paper describes how to compute equations of plane models of minimal Du Val double planes of general type with $p_g=q=1$ and $K^2=2,\mathrm{.}\mathrm{.}\mathrm{.},8.$ A double plane with $K^2=8$ having bicanonical map not composed with the associated involution is also constructed. The computations are done using the algebra system Magma.