On the field of definition of $$p$$-torsion points on elliptic curves over the rationals

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Galois representations attached to elliptic curves with complex multiplication (2018, background): “A classification of p-adic (or even mod p) images attached to elliptic curves can yield many other results as an application (see for instance the introduction to [17], or other examples such as [14] [11], [7], [4], or [6]).”
Torsion of rational elliptic curves over cubic fields and sporadic points on $X_1(n)$ (2012, background): “Somewhat similar problems were studied by Fujita [8], who studied the possible torsion groups of rational elliptic curves over the compositum of all quadratic fields, by Lozano-Robledo [25], who studied the minimal degree of the field of definition of points of order p on rational elliptic curves an”