# Revision history [back]

### 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 + axy + cy = x^3 + bx^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=$2^255-19$

### 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 + axy + cy = x^3 + bx^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=$2^{255}-19$ 3 None

### How define Twisted Edwards elliptic curve ?

EllipticCurve in Sage has In Sage, EllipticCurve takes 2 or 5 parameters. parameters.

For 5 parameters EllipticCurve([a,b,c,d,e]) means: parameters, EllipticCurve([a, b, c, d, e]) means:

y^2 + axy a*x*y + cy c*y = x^3 + bx^2 b*x^2 + d*x + e.

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

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

What means "twisted"? does "twisted" mean?

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

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