A ruled residue theorem for function fields of elliptic curves

It is shown that a valuation of residue characteristic different from 2 and 3 on a field E has at most one extension to the function field of an elliptic curve over E, for which the residue field extension is transcendental but not ruled. The cases where such an extension is present are characterised.(c) 2023 Elsevier B.V. All rights reserved.