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

Stability of ideal lattices from quadratic number fields