Realizing Rational Representations in Mordell-Weil Groups
  Let G be a finite group and V a finite-dimensional rational G-representation. We ask whether there exists a finite Galois extension L/K of number fields with Galois group G, an elliptic curve E/K, and a G-submodule of E(L) tensor Q isomorphic to V. 
Bo-Hae Im and Michael Larsen