Galois Lines for Normal Elliptic Space Curves, II

Abstract

For each linearly normal elliptic curve C ⊂ ℙ3, we determine Galois lines and their arrangement. We prove that the curve C has exactly six V4-lines. In case j(C) = 1, it has eight Z4-lines in addition. The V4-lines form the edges of a tetrahedron. In case j(C) = 1, for each vertex of the tetrahedron, there exist exactly two Z4-lines passing through it. As a corollary we obtain that each plane quartic curve of genus 1 does not have more than one Galois point.