All Items 1 Collection 1 The Octagon 1 Contributor 2 Cox, David A. (Department of Mathematics and Statistics, Amherst College) 1 Hyde, Trevor (Department of Mathematics, University of Michigan) 1 Topic 1 Galois theory 1 Part Of 1 The Amherst College Octagon 1 Genre 1 Article 1 Subject 1 Galois theory 1 The Galois theory of the lemniscate Cox, David A. (Department of Mathematics and Statistics, Amherst College) This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by proving the irreducibility of lemnatomic polynomials, which are analogs of cyclotomic polynomials. We also discuss Abelâ€™s theorem on the lemniscate and explain how lemnatomic polynomials relate to Chebyshev polynomials. The Galois theory of the lemniscate