Title: Integrality of twisted L-values of elliptic curves Abstract: In the context of the generalised Birch and Swinnerton-Dyer conjecture, one considers the value at s=1 of the L-function of an elliptic curve E/\mathbb{Q} twisted by a Dirichlet character \chi. When normalised with a period, one obtains an algebraic number \mathscr{L}(E,\chi). In joint work with Hanneke Wiersema, we determine under what conditions \mathscr{L}(E,\chi) is an algebraic integer.