Parameters

SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc6)
d = K(0x9baa8)
E = EllipticCurve(K, (K(-1/48) * (a^2 + 14*a*d + d^2),K(1/864) * (a + d) * (-a^2 + 34*a*d - d^2)))
def to_weierstrass(a, d, x, y):
	return ((5*a + a*y - 5*d*y - d)/(12 - 12*y), (a + a*y - d*y -d)/(4*x - 4*x*y))
def to_twistededwards(a, d, u, v):
	y = (5*a - 12*u - d)/(-12*u - a + 5*d)
	x = (a + a*y - d*y -d)/(4*v - 4*v*y)
	return (x, y)
G = E(*to_weierstrass(a, d, K(0x20), K(0x7d67e841dc4c467b605091d80869212f9ceb124bf726973f9ff048779e1d614e62ae2ece5057b5dad96b7a897c1d72799261134638750f4f0cb91027543b1c5e)))
E.set_order(0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa7e50809efdabbb9a624784f449545f0dcea5ff0cb800f894e78d1cb0b5f0189 * 0x04)
# This curve is a Weierstrass curve (SAGE does not support TwistedEdwards curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_twistededwards functions to convert the points.

JSON

{
  "name": "numsp512t1",
  "desc": "",
  "form": "TwistedEdwards",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7",
    "bits": 512
  },
  "params": {
    "a": {
      "raw": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc6"
    },
    "d": {
      "raw": "0x9baa8"
    }
  },
  "generator": {
    "x": {
      "raw": "0x20"
    },
    "y": {
      "raw": "0x7d67e841dc4c467b605091d80869212f9ceb124bf726973f9ff048779e1d614e62ae2ece5057b5dad96b7a897c1d72799261134638750f4f0cb91027543b1c5e"
    }
  },
  "order": "0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa7e50809efdabbb9a624784f449545f0dcea5ff0cb800f894e78d1cb0b5f0189",
  "cofactor": "0x04"
}