Parameters

Sources

• New explicit conditions of elliptic curve traces for FR-reduction

Characteristics

• j-invariant:
  440272393887005668066631560682754612404586866761175876059753922514267720
• Trace of Frobenius:
  3
• Discriminant:
  593429117302964579429108757221723198682714090669918720847187531278976024
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1456268479172808959148733486940327264608218463421238003553122264354852868
• CM-discriminant:
  -211
• Conductor:
  166153499473114484112975882535035935

SAGE

p = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007
K = GF(p)
a = K(0xd149265d4687dcab1f2046e0947e51ac5e8e7f25916d35539d4df2e9017a)
b = K(0x489e7783a1f584712bd4f6d48cf2d1ca2c975678936e639083991c5fc369)
E = EllipticCurve(K, (a, b))
G = E(0x1d871a744f1e02ed15d7d84abd95e80476e6307085f12dba27092ff06d60, 0x5c0c8bae9661303107b0077949dee16a7f6dde4982657b9196de23d9f9d0)
E.set_order(0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005 * 0x01)

PARI/GP

p = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007
a = Mod(0xd149265d4687dcab1f2046e0947e51ac5e8e7f25916d35539d4df2e9017a, p)
b = Mod(0x489e7783a1f584712bd4f6d48cf2d1ca2c975678936e639083991c5fc369, p)
E = ellinit([a, b])
E[16][1] = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005 * 0x01
G = [Mod(0x1d871a744f1e02ed15d7d84abd95e80476e6307085f12dba27092ff06d60, p), Mod(0x5c0c8bae9661303107b0077949dee16a7f6dde4982657b9196de23d9f9d0, p)]

JSON

{
  "name": "mnt5/1",
  "desc": "",
  "sources": [
    {
      "name": "New explicit conditions of elliptic curve traces for FR-reduction",
      "url": "https://dspace.jaist.ac.jp/dspace/bitstream/10119/4432/1/73-48.pdf"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007",
    "bits": 240
  },
  "params": {
    "a": {
      "raw": "0xd149265d4687dcab1f2046e0947e51ac5e8e7f25916d35539d4df2e9017a"
    },
    "b": {
      "raw": "0x489e7783a1f584712bd4f6d48cf2d1ca2c975678936e639083991c5fc369"
    }
  },
  "generator": {
    "x": {
      "raw": "0x1d871a744f1e02ed15d7d84abd95e80476e6307085f12dba27092ff06d60"
    },
    "y": {
      "raw": "0x5c0c8bae9661303107b0077949dee16a7f6dde4982657b9196de23d9f9d0"
    }
  },
  "order": "0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "593429117302964579429108757221723198682714090669918720847187531278976024",
    "j_invariant": "440272393887005668066631560682754612404586866761175876059753922514267720",
    "trace_of_frobenius": "3",
    "embedding_degree": "1456268479172808959148733486940327264608218463421238003553122264354852868",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-211",
    "conductor": "166153499473114484112975882535035935"
  }
}