= Bilinear degree pairing for elliptic-curve homomorphisms
{title2=$B(\phi,\psi)=\tfrac12(\deg(\phi+\psi)-\deg\phi-\deg\psi)$}
With zero degree assigned to the zero element of the <homomorphism group of elliptic curves>, the <degree parallelogram law> makes this symmetric pairing additive in both arguments. Its diagonal is the <degree of an isogeny>; it is positive definite on every finite-dimensional rational span after extension to the <real numbers>. The integral polarization $2B(\phi,\psi)$ is integer-valued, while $B$ can be half-integral. For instance, if an <elliptic curve> has an automorphism $\omega$ with $\omega^2+\omega+1=0$, then $1+\omega=-\omega^2$ has degree one, so $B(1,\omega)=-1/2$.
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