The Million Dollar Curve

Parameters

SAGE

p = 0xf13b68b9d456afb4532f92fdd7a5fd4f086a9037ef07af9ec13710405779ec13
K = GF(p)
d = K(0x571304521965b68a7cdfbfccfb0cb9625f1270f63f21f041ee9309250300cf89)
E = EllipticCurve(K, (0, K(2 * (1 + d)/(1 - d)^2), 0, K(1/(1 - d)^2), 0))
E.set_order(0x3c4eda2e7515abed14cbe4bf75e97f534fb38975faf974bb588552f421b0f7fb * 0x04)
# This curve is a Weierstrass curve (SAGE does not support Edwards curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_edwards functions to convert the points.

JSON

{
  "name": "MDC201601",
  "desc": "The Million Dollar Curve",
  "form": "Edwards",
  "field": {
    "type": "Prime",
    "p": "0xf13b68b9d456afb4532f92fdd7a5fd4f086a9037ef07af9ec13710405779ec13",
    "bits": 256
  },
  "params": {
    "c": {
      "raw": "0x01"
    },
    "d": {
      "raw": "0x571304521965b68a7cdfbfccfb0cb9625f1270f63f21f041ee9309250300cf89"
    }
  },
  "generator": {
    "x": {
      "raw": "0xb681886a7f903b83d85b421e03cbcf6350d72abb8d2713e2232c25bfee68363b"
    },
    "y": {
      "raw": "0xca6734e1b59c0b0359814dcf6563da421da8bc3d81a93a3a7e73c355bd2864b5"
    }
  },
  "order": "0x3c4eda2e7515abed14cbe4bf75e97f534fb38975faf974bb588552f421b0f7fb",
  "cofactor": "0x04"
}