Explicit-Formulas Database
Genus-1 curves over large-characteristic fields

Montgomery curves

An elliptic curve in Montgomery form [database entry; Sage verification script; Sage output] has parameters a b and coordinates x y satisfying the following equations:
  b*y^2=x^3+a*x^2+x

Representations for fast computations

XZ coordinates [more information] represent x y as X Z satisfying the following equations:
  x=X/Z