Backprop Through a Sharpened Sigmoid

A neuron squashes its raw score $z$ with a sharpened sigmoid — an ordinary logistic curve with a gain of $2$ baked into the exponent:

$a(z) = \frac{1}{1 + e^{-2z}}$

Backpropagation needs $a'(z)$ at the point where the neuron is perfectly undecided, $z = 0$.

Given $e^{0} = 1$, what is $a'(0)$?