For each linearly normal elliptic curve $C$ in $\mathbb P^3$, we determine Galois lines and their arrangement. The results are as follows: the curve $C$ has just six $V_4$-lines and in case $j(C)=1$, it has eight $Z_4$-lines in addition. The $V_4$-lines form the edges of a tetrahedron, in case $j(C)=1$, for each vertex of the tetrahedron, there exist just two $Z_4$-lines passing through it. We obtain as a corollary that each plane quartic curve of genus one does not have more than one Galois point.
Categories: math.AG