  We study the behaviour of automorphic L-Invariants associated to cuspidal
representations of GL(2) of cohomological weight 0 under abelian base change
and Jacquet-Langlands lifts to totally definite quaternion algebras.
  Under a standard non-vanishing hypothesis on automorphic L-functions and some
technical restrictions on the automorphic representation and the base field we
get a simple proof of the equality of automorphic and arithmetic L-invariants.
This together with Spiess' results on p-adic L-functions yields a new proof of
the exceptional zero conjecture for modular elliptic curves - at least, up to
sign.
