How define Twisted Edwards elliptic curve ?

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In Sage, EllipticCurve takes 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.

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

This equation has a term in $x^2y^2$ which does not exist in Sage EllipticCurve parameters.

What does "twisted" mean?

How to define $\frac{121665}{121666}$ ?

I must multiply 121665 but inverted 121666 in field? Field is with prime p=$2^{255}-19$.