Let $E:y^2=x^3+Ax+B$ be an integral, minimal model for an elliptic curve over $\mathbb{Q}$. The discriminant of $E$ is $\Delta = -2^4(4A^3+27B^2)$ so $E$ always has bad reduction at $p=2$. A search on the LMFDB suggests that this reduction is always additive. Is this the case, and if so why?
My current understanding is that a curve has additive reduction at $p$ if the reduced curve has a triple root. This occurs for some curves of this form, e.g $E_1: y^2=x^3+2$, but not for all, e.g $E_2:y^2=x^3+1$. Both examples have additive reduction at 2 however. Is there perhaps a more general definition?
Many thanks for any guidance provided.