An isogeny $\phi: (E,O)\to (E',O')$ between elliptic curves $E$ and $E'$ is a morphism that satisfies $\phi(O)=O'$.
It is known that $\phi$ is a group homomorphism.
Could you provide an example of a group homomorphism between elliptic curves that is not an isogeny?
Thank you in advance for your example.