After replacing $(a,b,c)$ by an equivalent triple obtained by permuting the entries and changing signs, assume that $b$ is even and $a \equiv -1 \pmod 4$. Let $E_{a,b,p}$ be the elliptic curve over $\mathbb{Q}$ given by
Then every minimal Weierstrass model of $E_{a,b,p}$ has either good or multiplicative reduction at every rational prime. Equivalently, $E_{a,b,p}$ is semistable over $\mathbb{Q}$.