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