A quadratic twist of an elliptic curve 
over a field 
is an elliptic curve 
that becomes isomorphic
to 
over a quadratic extension of 
but need not be isomorphic
to 
over 
.
If the field characteristic is not 2 and
 |
then one model for the twist by 
is
 |
It becomes isomorphic to 
over 
, and multiplying 
by a nonzero square gives a twist isomorphic
over 
.
