  We calculated, within the Gross-Pitaevskii formalism, the critical number of
atoms for Bose-Einstein condensates with two-body attractive interactions in
cylindrical traps with different frequency ratios. In particular, by using the
trap geometries considered by the JILA group [Phys. Rev. Lett. 86, 4211
(2001)], we show that the theoretical maximum critical numbers are given
approximately by $N_c = 0.55 ({l_0}/{|a|})$. Our results also show that, by
exchanging the frequencies $\omega_z$ and $\omega_\rho$, the geometry with
$\omega_\rho < \omega_z$ favors the condensation of larger number of particles.
We also simulate the time evolution of the condensate when changing the ground
state from $a=0$ to $a<0$ using a 200ms ramp. A conjecture on higher order
nonlinear effects is also added in our analysis with an experimental proposal
to determine its signal and strength.
