Parameters

Sources

• A Family of Implementation-Friendly BN Elliptic Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  186496302581962721809830439849867378820456264884631045871326327118225203759963374092295
• Discriminant:
  34780870876742995377456858134373496984033068311331682913917171552933960384313251034752424287877192201334219790531446172327873978399527076876359580494778958227471204544936275
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  186496302581962721809830439849867378820456242583880530431255347119471774686354153144323

SAGE

p = 0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2808400041FFFE73FFF7C000210000000000001380004DFFFD90000000000000000000000013
K = GF(p)
a = K(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
b = K(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002)
E = EllipticCurve(K, (a, b))
G = E(0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2808400041FFFE73FFF7C000210000000000001380004DFFFD90000000000000000000000012, 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001)
E.set_order(0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2807E0003EFFFE85FFF820001F80000000000010800041FFFDF000000000000000000000000D * 0x01)

PARI/GP

p = 0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2808400041FFFE73FFF7C000210000000000001380004DFFFD90000000000000000000000013
a = Mod(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002, p)
E = ellinit([a, b])
E[16][1] = 0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2807E0003EFFFE85FFF820001F80000000000010800041FFFDF000000000000000000000000D * 0x01
G = [Mod(0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2808400041FFFE73FFF7C000210000000000001380004DFFFD90000000000000000000000012, p), Mod(0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001, p)]

JSON

{
  "name": "bn574",
  "desc": "",
  "sources": [
    {
      "name": "A Family of Implementation-Friendly BN Elliptic Curves",
      "url": "https://eprint.iacr.org/2010/429"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2808400041FFFE73FFF7C000210000000000001380004DFFFD90000000000000000000000013",
    "bits": 574
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002"
    }
  },
  "generator": {
    "x": {
      "raw": "0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2808400041FFFE73FFF7C000210000000000001380004DFFFD90000000000000000000000012"
    },
    "y": {
      "raw": "0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
    }
  },
  "order": "0x2400023FFFFB7FFF4C00002400167FFFEE01AEE014423FAEFFFB5C000A200050FFFF2807E0003EFFFE85FFF820001F80000000000010800041FFFDF000000000000000000000000D",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "34780870876742995377456858134373496984033068311331682913917171552933960384313251034752424287877192201334219790531446172327873978399527076876359580494778958227471204544936275",
    "j_invariant": "0",
    "trace_of_frobenius": "186496302581962721809830439849867378820456264884631045871326327118225203759963374092295",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "186496302581962721809830439849867378820456242583880530431255347119471774686354153144323"
  }
}