I am trying to solve exercise 7.5. b) from Silverman's book, namely to find a minimal model of the elliptic curve $E: y^2+y=x^3$, over $\mathbb{Q}_3(\pi,\nu)$ where $\pi^2=\sqrt{-3}$ and $\nu^3=2$. Note that the discriminant $\Delta=-3^3$ and the curve has good reduction over the above-mentioned extension.
I want to simply find a change of variables $(x,y)\to(x',y')$ that would work, without using Tate's algorithm.
A Weierstrass equation is $y^2=x^3+2^4$.