For which fields can a, minimal Weierstrass equation of elliptic curve be defined?
If $K$ is a local field, valuation takes discrete value, so we can define a minimal Weierstrass equation.
But I heard if $K＝ \mathbb{Q}$, we can also define minimal Weierstrass equation.
For which fields can we define a minimal Weierstrass equation of elliptic curve? (I guess we can do so for local fields and $\mathbb{Q}$ only, I can't define it on $\mathbb{C}$ or $\mathbb{F}_q$ or..)