Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.5
• j-invariant:
  631303702419486211765940489888844177839080623666750326568416307553
• Trace of Frobenius:
  4460773185803614235113038911974753
• Discriminant:
  14205275590849738147256021798014879924249460148276819971134307874821
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  3786937155409058797925422999318487268761257723721792865232760161093
• CM-discriminant:
  10098499081090823461134461331515967536954415864462859344966997754499
• Conductor:
  3

SAGE

p = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff
K = GF(p)
a = K(0x68a5e62ca9ce6c1c299803a6c1530b514e182ad8b0042a59cad29f43)
b = K(0x2580f63ccfe44138870713b1a92369e33e2135d266dbb372386c400b)
E = EllipticCurve(K, (a, b))
G = E(0xd9029ad2c7e5cf4340823b2a87dc68c9e4ce3174c1e6efdee12c07d, 0x58aa56f772c0726f24c6b89e4ecdac24354b9e99caa3f6d3761402cd)
E.set_order(0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f * 0x1)

PARI/GP

p = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff
a = Mod(0x68a5e62ca9ce6c1c299803a6c1530b514e182ad8b0042a59cad29f43, p)
b = Mod(0x2580f63ccfe44138870713b1a92369e33e2135d266dbb372386c400b, p)
E = ellinit([a, b])
E[16][1] = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f * 0x1
G = [Mod(0xd9029ad2c7e5cf4340823b2a87dc68c9e4ce3174c1e6efdee12c07d, p), Mod(0x58aa56f772c0726f24c6b89e4ecdac24354b9e99caa3f6d3761402cd, p)]

JSON

{
  "name": "brainpoolP224r1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.5",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff",
    "bits": 224
  },
  "params": {
    "a": {
      "raw": "0x68a5e62ca9ce6c1c299803a6c1530b514e182ad8b0042a59cad29f43"
    },
    "b": {
      "raw": "0x2580f63ccfe44138870713b1a92369e33e2135d266dbb372386c400b"
    }
  },
  "generator": {
    "x": {
      "raw": "0xd9029ad2c7e5cf4340823b2a87dc68c9e4ce3174c1e6efdee12c07d"
    },
    "y": {
      "raw": "0x58aa56f772c0726f24c6b89e4ecdac24354b9e99caa3f6d3761402cd"
    }
  },
  "order": "0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "631303702419486211765940489888844177839080623666750326568416307553",
    "anomalous": false,
    "cm_disc": "10098499081090823461134461331515967536954415864462859344966997754499",
    "conductor": "3",
    "discriminant": "14205275590849738147256021798014879924249460148276819971134307874821",
    "embedding_degree": "3786937155409058797925422999318487268761257723721792865232760161093",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 6,
        "least": 2,
        "r": 3
      },
      {
        "full": 10,
        "least": 2,
        "r": 5
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "4460773185803614235113038911974753"
  }
}