Real Quadratic Fields In Which Every Non-Maximal Order Has Relative Class Number Greater Than One

Abstract

Cohn asks if for every real quadratic field Q(m) with discriminant d there exists a non-maximal order corresponding to f > 1 such that the relative class number Hd(f) = h(f2d)/h(d) is one. We prove that when m = 46 (and in seven other cases) there is no such order.