Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.6
• j-invariant:
  631303702419486211765940489888844177839080623666750326568416307553
• Trace of Frobenius:
  4460773185803614235113038911974753
• Discriminant:
  8915718169748412708727830550973603735673450174737989195928269078490
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  3786937155409058797925422999318487268761257723721792865232760161093
• CM-discriminant:
  10098499081090823461134461331515967536954415864462859344966997754499
• Conductor:
  3

SAGE

p = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff
K = GF(p)
a = K(0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0fc)
b = K(0x4b337d934104cd7bef271bf60ced1ed20da14c08b3bb64f18a60888d)
E = EllipticCurve(K, (a, b))
G = E(0x6ab1e344ce25ff3896424e7ffe14762ecb49f8928ac0c76029b4d580, 0x374e9f5143e568cd23f3f4d7c0d4b1e41c8cc0d1c6abd5f1a46db4c)
E.set_order(0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f * 0x1)

PARI/GP

p = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff
a = Mod(0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0fc, p)
b = Mod(0x4b337d934104cd7bef271bf60ced1ed20da14c08b3bb64f18a60888d, p)
E = ellinit([a, b])
E[16][1] = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f * 0x1
G = [Mod(0x6ab1e344ce25ff3896424e7ffe14762ecb49f8928ac0c76029b4d580, p), Mod(0x374e9f5143e568cd23f3f4d7c0d4b1e41c8cc0d1c6abd5f1a46db4c, p)]

JSON

{
  "name": "brainpoolP224t1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.6",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff",
    "bits": 224
  },
  "params": {
    "a": {
      "raw": "0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0fc"
    },
    "b": {
      "raw": "0x4b337d934104cd7bef271bf60ced1ed20da14c08b3bb64f18a60888d"
    }
  },
  "generator": {
    "x": {
      "raw": "0x6ab1e344ce25ff3896424e7ffe14762ecb49f8928ac0c76029b4d580"
    },
    "y": {
      "raw": "0x374e9f5143e568cd23f3f4d7c0d4b1e41c8cc0d1c6abd5f1a46db4c"
    }
  },
  "order": "0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "631303702419486211765940489888844177839080623666750326568416307553",
    "anomalous": false,
    "cm_disc": "10098499081090823461134461331515967536954415864462859344966997754499",
    "conductor": "3",
    "discriminant": "8915718169748412708727830550973603735673450174737989195928269078490",
    "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"
  }
}