  Recent work demonstrated that breaking the up-down symmetry of tokamak flux
surfaces removes a constraint that limits intrinsic momentum transport, and
hence toroidal rotation, to be small. We show, through MHD analysis, that
ellipticity is most effective at introducing up-down asymmetry throughout the
plasma. We detail an extension to GS2, a local $\delta f$ gyrokinetic code that
self-consistently calculates momentum transport, to permit up-down asymmetric
configurations. Tokamaks with tilted elliptical poloidal cross-sections were
simulated to determine nonlinear momentum transport. The results, which are
consistent with experiment in magnitude, suggest that a toroidal velocity
gradient, $(\partial u_{\zeta i} / \partial \rho) / v_{th i}$, of 5% of the
temperature gradient, $(\partial T_{i} / \partial \rho) / T_{i}$, is
sustainable. Here $v_{th i}$ is the ion thermal speed, $u_{\zeta i}$ is the ion
toroidal mean flow, $\rho$ is the minor radial coordinate normalized to the
tokamak minor radius, and $T_{i}$ is the ion temperature. Since other intrinsic
momentum transport mechanisms scale poorly to larger machines, these results
indicate that up-down asymmetry is the most feasible method to generate the
current experimentally-measured rotation levels in reactor-sized devices.
