  We present a new general relativistic hydrodynamics code specifically
designed to study magneto-rotational, relativistic, stellar core collapse. The
code is an extension of an existing (and thoroughly tested) hydrodynamics code,
which has been applied in the recent past to study relativistic rotational core
collapse. It is based on the conformally-flat approximation of Einstein's field
equations and conservative formulations for the magneto-hydrodynamics
equations. As a first step towards magneto-rotational core collapse simulations
the code assumes a passive (test) magnetic field. The paper is focused on the
description of the technical details of the numerical implementation, with
emphasis on the magnetic field module. A number of code tests are presented and
discussed, along with a representative core collapse simulation.
