The degrees of points with rational j-invariant on X0(n) and X1(n) are classified for all n, unconditionally for infinitely occurring degrees and assuming Zywina's conjecture for finitely occurring ones.
Torsion of rational elliptic curves over quartic Galois number fields
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Degrees of points with rational $j$-invariant on $X_{0}(n)$ and $X_{1}(n)$
The degrees of points with rational j-invariant on X0(n) and X1(n) are classified for all n, unconditionally for infinitely occurring degrees and assuming Zywina's conjecture for finitely occurring ones.