  The V_4-lines for each linearly normal space elliptic curve form the edges of
a tetrahedron, however in case the elliptic curve has j=12^3, there exist
Z_4-lines in addition. We show the arrangement of V_4 and Z_4-lines explicitly
for the curve. As a corollary we obtain that each irreducible quartic curve
with genus one has at most two Galois points.
