### How define Twisted Edwards elliptic curve ?

EllipticCurve in Sage has 2 or 5 parameters.
For 5 parameters EllipticCurve([a,b,c,d,e]) means:
y^2 + a*x*y + c*y = x^3 + b*x^2 + d*x + e

Ed25519 (for example for Monero) is defined by $-x^2+y^2=1-\frac{121665}{121666}x^2y^2$

There exists part x^2y^2 which not exists in Sage EllipticCurve parameters.
What means "twisted"?
How define $\frac{121665}{121666}$ ? I must multiply 121665 bu inverted 121666 in field? Field is with prime ~~p=$2^255-19$~~p=$2^{255}-19$