Curve from https://eprint.iacr.org/2013/647.pdf

Parameters

SAGE

p = 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF45
K = GF(p)
A = K(0x081806)
B = K(0x01)
E = EllipticCurve(K, ((3 - A^2)/(3 * B^2), (2 * A^3 - 9 * A)/(27 * B^3)))
def to_weierstrass(A, B, x, y):
	return (x/B + A/(3*B), y/B)
def to_montgomery(A, B, u, v):
	return (B * (u - A/(3*B)), B*v)
G = E(*to_weierstrass(A, B, K(0x05), K(0x2fbdc0ad8530803d28fdbad354bb488d32399ac1cf8f6e01ee3f96389b90c809422b9429e8a43dbf49308ac4455940abe9f1dbca542093a895e30a64af056fa5)))
E.set_order(0x100000000000000000000000000000000000000000000000000000000000000017B5FEFF30C7F5677AB2AEEBD13779A2AC125042A6AA10BFA54C15BAB76BAF1B * 0x08)
# This curve is a Weierstrass curve (SAGE does not support Montgomery curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_montgomery functions to convert the points.

JSON

{
  "name": "M-511",
  "desc": "Curve from https://eprint.iacr.org/2013/647.pdf",
  "form": "Montgomery",
  "field": {
    "type": "Prime",
    "p": "0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF45",
    "bits": 511
  },
  "params": {
    "a": {
      "raw": "0x081806"
    },
    "b": {
      "raw": "0x01"
    }
  },
  "generator": {
    "x": {
      "raw": "0x05"
    },
    "y": {
      "raw": "0x2fbdc0ad8530803d28fdbad354bb488d32399ac1cf8f6e01ee3f96389b90c809422b9429e8a43dbf49308ac4455940abe9f1dbca542093a895e30a64af056fa5"
    }
  },
  "order": "0x100000000000000000000000000000000000000000000000000000000000000017B5FEFF30C7F5677AB2AEEBD13779A2AC125042A6AA10BFA54C15BAB76BAF1B",
  "cofactor": "0x08"
}