An Edwards curve over a field 
of field characteristic
other than 2 is the affine plane curve
 |
(1)
|
where 
and 
. Edwards (2007) introduced the
underlying elliptic curve normal form, and Bernstein
and Lange (2007) developed the modern one-parameter form above. For points 
and 
, the elliptic
curve group law is 
,
where
 |  |  |
(2)
|
 |  |  |
(3)
|
The identity element is 
, and the inverse element
of 
is 
. If 
is a nonsquare in 
, the addition formulas are complete (Bernstein and Lange 2007).
An Edwards curve is the 
special case of a twisted Edwards curve.
