This is the curve parametrized by x=cos(t), y=sin(t), z=1/(1+t^2) from t=-2pi to t=2pi. One .stl file has the equations on the curve, the second does not.
This model was designed and printed by my WLU summer research student Ryan McDonnell ('17).
We printed this curve on a FormLabs Form 1+ liquid resin printer. It was printed in black resin (0.1mm slices), The print was excellent in both cases. (The .form file we used is included.)
We think this curve could also be successfully printed on a MakerBot, (or other plastic filament printer) but have not tried this yet.