Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.9
• j-invariant:
  358066247632993218655312856437643774447933684237000889712532007541779113891565375554334303101086
• Trace of Frobenius:
  1829129012274291271856083956306349739816241699607
• Discriminant:
  1358401829173490165066196853884775272351426867124642504866990308858277224964072636606742251556422
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1763593322239166354161909842446019520889512772717686063760686124016784784845843468355685258203920
• CM-discriminant:
  7054373288956665416647639369784078083558051090876231642079567369882707391252292922642189757914501
• Conductor:
  1

SAGE

p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
K = GF(p)
a = K(0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4)
b = K(0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6)
E = EllipticCurve(K, (a, b))
G = E(0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611, 0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1)
E.set_order(0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311 * 0x1)

PARI/GP

p = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
a = Mod(0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4, p)
b = Mod(0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6, p)
E = ellinit([a, b])
E[16][1] = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311 * 0x1
G = [Mod(0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611, p), Mod(0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1, p)]

JSON

{
  "name": "brainpoolP320r1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.9",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27",
    "bits": 320
  },
  "params": {
    "a": {
      "raw": "0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4"
    },
    "b": {
      "raw": "0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6"
    }
  },
  "generator": {
    "x": {
      "raw": "0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611"
    },
    "y": {
      "raw": "0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1"
    }
  },
  "order": "0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "358066247632993218655312856437643774447933684237000889712532007541779113891565375554334303101086",
    "anomalous": false,
    "cm_disc": "7054373288956665416647639369784078083558051090876231642079567369882707391252292922642189757914501",
    "conductor": "1",
    "discriminant": "1358401829173490165066196853884775272351426867124642504866990308858277224964072636606742251556422",
    "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"
  }
}