The analysis of type IIB flux vacua on warped Calabi--Yau orientifolds
becomes considerably involved for a large number of complex structure fields.
We however show that, for a quadratic flux superpotential, one can devise
simplifying schemes which effectively reduce the large number of equations down
to a few. This can be achieved by imposing the vanishing of certain flux quanta
in the large complex structure regime, and then choosing the remaining quanta
to respect the symmetries of the underlying prepotential. One can then
implement an algorithm to find large families of flux vacua with a fixed flux
tadpole, independently of the number of fields. We illustrate this approach in
a Calabi--Yau manifold with 51 complex structure moduli, where several
reduction schemes can be implemented in order to explicitly solve the vacuum
equations for that sector. Our findings display a
flux-tadpole-to-stabilized-moduli ratio that is marginally above the bound
proposed by the Tadpole Conjecture, and we discuss several effects that would
take us below such a bound.Comment: 42 pages + appendices, 3 figure