  We study numerically an $s$-wave holographic superconductor from an anti-de
Sitter-Einstein-Born-Infeld black hole with backreaction in the context of the
AdS/CFT correspondence. By introducing a parameter $G$ to tune the effects of
the backreaction, we can study non-perturbatively how the condensation
properties and conductivity of the superconductor change as the backreaction
increases. We find that for small values of $G$, increasing the nonlinearity of
the Born-Infeld model makes the formation of the condensate harder --
consistent with previous results reported in the literature -- while for values
of $G$ close to one, the opposite effect occurs; increasing the nonlinearity
slightly facilitates its formation. We also determine how the ratio
$\omega_g/T_c$ varies for different intensities of nonlinearity and
backreaction, showing in particular that large deviations from the so-called
universal value arise as backreaction becomes stronger.
