= Solution
An <elliptic curve> has <good reduction of an elliptic curve> at $p$ if it admits a <Weierstrass equation of an elliptic curve> over $\mathbb Z_p$ whose reduced projective cubic is nonsingular. Equivalently its minimal discriminant is a $p$-adic unit.
For the given integral short equation,
$$
\Delta=-16\cdot27\cdot225^2=-2^4\,3^7\,5^4.
$$
It therefore directly supplies good reduction outside $2,3,5$. These three primes cannot be rescued by changing the model. An admissible change of <Weierstrass model> changes the discriminant by a twelfth power, so its valuation changes by a multiple of twelve. The displayed valuations $4,7,4$ are not congruent to zero modulo twelve. No integral model can have unit discriminant at any of those primes. \b[The good primes are exactly $p\notin\{2,3,5\}$.]
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