  We investigate the number of nodal intersections of random Gaussian Laplace
eigenfunctions on the standard three-dimensional flat torus with a fixed smooth
reference curve, which has nowhere vanishing curvature. The expected
intersection number is universally proportional to the length of the reference
curve, times the wavenumber, independent of the geometry. Our main result gives
a bound for the variance, if either the torsion of the curve is nowhere zero or
if the curve is planar.
