= Degree of an isogeny from its x-coordinate map
{title2=$\deg\phi=\max(\deg A,\deg B)$}
For an <isogeny of elliptic curves> $\phi:E_1\to E_2$, write $x_2\circ\phi=A(x_1)/B(x_1)$ with <coprime> <polynomials> $A,B$. Each $x_i:E_i\to\mathbb P^1$ is a two-to-one <finite morphism>, and <function field> degrees multiply in a tower. Consequently $2\deg\phi=2\max(\deg A,\deg B)$. This computes the total degree, including an inseparable factor. The zero homomorphism is assigned degree zero separately.
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