Does the regular property of a curve depend on the parametrization used?

Question

For a given curve $C$, and two different parametrizations $\alpha_1$ and $\alpha_2$ of $C$. Can $\alpha_1$ imply that $C$ is regular and $\alpha_2$ imply that $C$ is not regular ? If this is true how is this possible and what can we conclude about $C$ ?

Answer 1

This can not be true, any reparameterization of a regular curve is regular. And this https://math.stackexchange.com/a/484656/142677 answer along with the link in it is a better explanation than I could ever write.