  We study semi-stable ideal lattices coming from real quadratic number fields.
Specifically, we demonstrate infinite families of semi-stable and unstable
ideal lattices of trace type, establishing explicit conditions on the canonical
basis of an ideal that ensure stability; in particular, our result implies that
an ideal lattice of trace type coming from a real quadratic field is
semi-stable with positive probability. We also briefly discuss the connection
between stability and well-roundedness of Euclidean lattices.
