What is an Isogeny in Complex Numbers?

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Can someone give a simple explanation what it is meant to be an isogeny in complex numbers? I know that it is a homomorphism between two elliptic curves of the form $\mathbb{C}/L$ where $L$ is a lattice. But how can we show that a given map is an isogeny and find the elements of its kernel? It would be good if you can explain this via an example.