Class numbers of the simplest cubic fields
Class numbers of the simplest cubic fields
Using the "simplest cubic fields" of D. Shanks, we give a modified proof and an extension of a result of Uchida, showing how to obtain cyclic cubic fields with class number divisible by <italic>n</italic>, for any <italic>n</italic>. Using 2-descents on elliptic curves, we obtain precise information on the 2-Sylow subgroups …