Parameters

Characteristics

• OID:
  1.2.840.10045.3.1.6
• Seed:
  7D7374168FFE3471B60A857686A19475D3BFA2FF
• j-invariant:
  753745430086077892322271754405460844839460634669491132164952757184512889
• Trace of Frobenius:
  543286227487037812274483689551665839
• Discriminant:
  882873045738548432559077267776614981148556437256582152685457545366799895

SAGE

p = 0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff
K = GF(p)
a = K(0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc)
b = K(0x255705fa2a306654b1f4cb03d6a750a30c250102d4988717d9ba15ab6d3e)
E = EllipticCurve(K, (a, b))
G = E(0x6768ae8e18bb92cfcf005c949aa2c6d94853d0e660bbf854b1c9505fe95a, 0x1607e6898f390c06bc1d552bad226f3b6fcfe48b6e818499af18e3ed6cf3)
E.set_order(0x7fffffffffffffffffffffff7fffff975deb41b3a6057c3c432146526551 * 0x1)

PARI/GP

p = 0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff
a = Mod(0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc, p)
b = Mod(0x255705fa2a306654b1f4cb03d6a750a30c250102d4988717d9ba15ab6d3e, p)
E = ellinit([a, b])
E[16][1] = 0x7fffffffffffffffffffffff7fffff975deb41b3a6057c3c432146526551 * 0x1
G = [Mod(0x6768ae8e18bb92cfcf005c949aa2c6d94853d0e660bbf854b1c9505fe95a, p), Mod(0x1607e6898f390c06bc1d552bad226f3b6fcfe48b6e818499af18e3ed6cf3, p)]

JSON

{
  "name": "prime239v3",
  "desc": "",
  "oid": "1.2.840.10045.3.1.6",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff",
    "bits": 239
  },
  "params": {
    "a": {
      "raw": "0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc"
    },
    "b": {
      "raw": "0x255705fa2a306654b1f4cb03d6a750a30c250102d4988717d9ba15ab6d3e"
    }
  },
  "generator": {
    "x": {
      "raw": "0x6768ae8e18bb92cfcf005c949aa2c6d94853d0e660bbf854b1c9505fe95a"
    },
    "y": {
      "raw": "0x1607e6898f390c06bc1d552bad226f3b6fcfe48b6e818499af18e3ed6cf3"
    }
  },
  "order": "0x7fffffffffffffffffffffff7fffff975deb41b3a6057c3c432146526551",
  "cofactor": "0x1",
  "characteristics": {
    "seed": "7D7374168FFE3471B60A857686A19475D3BFA2FF",
    "j_invariant": "753745430086077892322271754405460844839460634669491132164952757184512889",
    "discriminant": "882873045738548432559077267776614981148556437256582152685457545366799895",
    "trace_of_frobenius": "543286227487037812274483689551665839"
  }
}