A note on the trace of Frobenius for curves of the form y² = x³ + dx

Abstract

. An explicit description of the trace of Frobenius is given for any elliptic curve over Q of the form 𝑦 2 = 𝑥 3 + 𝑑𝑥 . This description leads to an algorithm which computes the trace at a cost of one modular exponentiation.