  In this note we consider questions about parametrisations of elliptic curves
defined over number fields by quotients of the upper half-plane by finite index
subgroups of SL_2(Z). We ask if we can choose such a parametrisation of an
elliptic curve to reflect the field over which it is defined: this can be
viewed as a generalisation of the Shimura-Taniyama-Weil conjecture.
