Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.10
• j-invariant:
  358066247632993218655312856437643774447933684237000889712532007541779113891565375554334303101086
• Trace of Frobenius:
  1829129012274291271856083956306349739816241699607
• Discriminant:
  1227797986910447087693861407896680306667211312863522948660645891506165614844254984237818878886705
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1763593322239166354161909842446019520889512772717686063760686124016784784845843468355685258203920
• CM-discriminant:
  7054373288956665416647639369784078083558051090876231642079567369882707391252292922642189757914501
• Conductor:
  1

SAGE

p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
K = GF(p)
a = K(0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e24)
b = K(0xa7f561e038eb1ed560b3d147db782013064c19f27ed27c6780aaf77fb8a547ceb5b4fef422340353)
E = EllipticCurve(K, (a, b))
G = E(0x925be9fb01afc6fb4d3e7d4990010f813408ab106c4f09cb7ee07868cc136fff3357f624a21bed52, 0x63ba3a7a27483ebf6671dbef7abb30ebee084e58a0b077ad42a5a0989d1ee71b1b9bc0455fb0d2c3)
E.set_order(0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311 * 0x1)

PARI/GP

p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
a = Mod(0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e24, p)
b = Mod(0xa7f561e038eb1ed560b3d147db782013064c19f27ed27c6780aaf77fb8a547ceb5b4fef422340353, p)
E = ellinit([a, b])
E[16][1] = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311 * 0x1
G = [Mod(0x925be9fb01afc6fb4d3e7d4990010f813408ab106c4f09cb7ee07868cc136fff3357f624a21bed52, p), Mod(0x63ba3a7a27483ebf6671dbef7abb30ebee084e58a0b077ad42a5a0989d1ee71b1b9bc0455fb0d2c3, p)]

JSON

{
  "name": "brainpoolP320t1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.10",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27",
    "bits": 320
  },
  "params": {
    "a": {
      "raw": "0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e24"
    },
    "b": {
      "raw": "0xa7f561e038eb1ed560b3d147db782013064c19f27ed27c6780aaf77fb8a547ceb5b4fef422340353"
    }
  },
  "generator": {
    "x": {
      "raw": "0x925be9fb01afc6fb4d3e7d4990010f813408ab106c4f09cb7ee07868cc136fff3357f624a21bed52"
    },
    "y": {
      "raw": "0x63ba3a7a27483ebf6671dbef7abb30ebee084e58a0b077ad42a5a0989d1ee71b1b9bc0455fb0d2c3"
    }
  },
  "order": "0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "358066247632993218655312856437643774447933684237000889712532007541779113891565375554334303101086",
    "anomalous": false,
    "cm_disc": "7054373288956665416647639369784078083558051090876231642079567369882707391252292922642189757914501",
    "conductor": "1",
    "discriminant": "1227797986910447087693861407896680306667211312863522948660645891506165614844254984237818878886705",
    "embedding_degree": "1763593322239166354161909842446019520889512772717686063760686124016784784845843468355685258203920",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 4,
        "least": 2,
        "r": 5
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "1829129012274291271856083956306349739816241699607"
  }
}