Parameters

Sources

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

Characteristics

• j-invariant:
  1217230860629624462533218875960633666717430508755963349556749378716290482
• Trace of Frobenius:
  3
• Discriminant:
  1165886697795797508768474941606426206406384333521273560872915843944307054
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1456268479172808959148733486940327264608218463421238003553122264354852868
• CM-discriminant:
  -211
• Conductor:
  166153499473114484112975882535035935

SAGE

p = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007
K = GF(p)
a = K(0x26caaced434c5a4c2c9c1b09e0ddc167548a95516e7c81b20702485c9809)
b = K(0x6031c89e2cdd91881dbd675beac3f3df8db1b8e0f45301215a01baf56ab3)
E = EllipticCurve(K, (a, b))
G = E(0x16e55a2ef696238a7aaf19e51b6a81e1582f28b4bcb6575ab4e0331e569b, 0x38de9844643fc9db3c568ec528983da16a177d56145a1d4bf88a2340d839)
E.set_order(0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005 * 0x01)

PARI/GP

p = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007
a = Mod(0x26caaced434c5a4c2c9c1b09e0ddc167548a95516e7c81b20702485c9809, p)
b = Mod(0x6031c89e2cdd91881dbd675beac3f3df8db1b8e0f45301215a01baf56ab3, p)
E = ellinit([a, b])
E[16][1] = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005 * 0x01
G = [Mod(0x16e55a2ef696238a7aaf19e51b6a81e1582f28b4bcb6575ab4e0331e569b, p), Mod(0x38de9844643fc9db3c568ec528983da16a177d56145a1d4bf88a2340d839, p)]

JSON

{
  "name": "mnt5/2",
  "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": "0x26caaced434c5a4c2c9c1b09e0ddc167548a95516e7c81b20702485c9809"
    },
    "b": {
      "raw": "0x6031c89e2cdd91881dbd675beac3f3df8db1b8e0f45301215a01baf56ab3"
    }
  },
  "generator": {
    "x": {
      "raw": "0x16e55a2ef696238a7aaf19e51b6a81e1582f28b4bcb6575ab4e0331e569b"
    },
    "y": {
      "raw": "0x38de9844643fc9db3c568ec528983da16a177d56145a1d4bf88a2340d839"
    }
  },
  "order": "0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "1165886697795797508768474941606426206406384333521273560872915843944307054",
    "j_invariant": "1217230860629624462533218875960633666717430508755963349556749378716290482",
    "trace_of_frobenius": "3",
    "embedding_degree": "1456268479172808959148733486940327264608218463421238003553122264354852868",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-211",
    "conductor": "166153499473114484112975882535035935"
  }
}