On the Deuring Polynomial for Drinfeld Modules in Legendre Form

Abstract

We study a family $ψ^λ$ of $\mathbb F_q[T]$-Drinfeld modules, which is a natural analog of Legendre elliptic curves. We then find a surprising recurrence giving the corresponding Deuring polynomial $H_{p(T)}(λ)$ characterising supersingular Legendre Drinfeld modules $ψ^λ$ in characteristic $p(T)$.

This article supersedes arXiv:1110.6076