Curve from https://ethresear.ch/t/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field/9957

Parameters

Characteristics

• j-invariant:
  0x1f40
• Discriminant:
  -0x08

SAGE

p = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
K = GF(p)
a = K(-0x05)
d = K(0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7)
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)
# No generator defined
E.set_order(0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1 * 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": "Bandersnatch",
  "desc": "Curve from https://ethresear.ch/t/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field/9957",
  "form": "TwistedEdwards",
  "field": {
    "type": "Prime",
    "p": "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001",
    "bits": 255
  },
  "params": {
    "a": {
      "raw": "-0x05"
    },
    "d": {
      "raw": "0x6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7"
    }
  },
  "order": "0x1cfb69d4ca675f520cce760202687600ff8f87007419047174fd06b52876e7e1",
  "cofactor": "0x04",
  "characteristics": {
    "j_invariant": "0x1f40",
    "discriminant": "-0x08"
  }
}