Galois lines for normal elliptic space curves

Let C be a curve, and l and l(0) be lines in the projective three space P-3. Consider a projection pi(l) : P-3 ... -> l(0) with center l, where l boolean AND l(0) = 0. Restricting pi(l) to C, we obtain a morphism pi(l)vertical bar c : C -> l(0) and an extension of fields (pi(l)vertical bar(C))* : k(l(0)) -> k(C). If this extension is Galois, then l is said to be a Galois line. We study the defining equations, automorphisms and the Galois lines for quartic curves, and give some applications to the theory of plane quartic curves.