= Solution
An <elliptic curve> over $\mathbb Q$ has <good reduction> at $p$ if it admits an integral <Weierstrass equation of an elliptic curve> over $\mathbb Z_p$ whose reduced projective cubic is a <smooth algebraic curve> over $\mathbb F_p$. Equivalently, its <Minimal Weierstrass equation> has a unit <elliptic-curve discriminant>, or its smooth proper model is an <elliptic curve> over the <valuation ring>. The existence of an appropriate integral model matters: a nonminimal equation can have discriminant divisible by $p$ even when the curve has <good reduction>. Equivalently,
$$
\boxed{E\text{ has good reduction at }p\iff v_p(\Delta_{\min})=0.}
$$
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