Galois lines for normal elliptic space curves, II

Abstract

For each linearly normal elliptic curve C ⊂ 3, 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 Z 4-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. © 2012 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.