Is an inflection point of an algebraic cuve intrinsic?

Question

On an algebraic curve $C$ in $P^2$ over a field $F$, a regular point $p\in C$ is called an inflection point if $I(p,C\cap L)>2$, where $L$ is the tangent line through $p$. I'm wondering is this concept independent of isomorphism? We know that it's invariant under projective maps.

Answer 1

A smooth curve $C$ of genus one admits the structure of an algebraic group (elliptic curve). In particular, one can translate by points on $C$; therefore, an inflection point can be translated to any other point of $C$, and the notion is not independent of isomorphism.