Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.3
• j-invariant:
  3145146591935622866306370409311868292910840518057952172666
• Trace of Frobenius:
  75885465139255996133178324439
• Discriminant:
  944310369424837272716401339845420116098509061277344316275
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  597708622988270780369375236783629788514982957389979358616
• CM-discriminant:
  19126675935624664971820007577303809627897222624878874449029
• Conductor:
  1

SAGE

p = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297
K = GF(p)
a = K(0x6a91174076b1e0e19c39c031fe8685c1cae040e5c69a28ef)
b = K(0x469a28ef7c28cca3dc721d044f4496bcca7ef4146fbf25c9)
E = EllipticCurve(K, (a, b))
G = E(0xc0a0647eaab6a48753b033c56cb0f0900a2f5c4853375fd6, 0x14b690866abd5bb88b5f4828c1490002e6773fa2fa299b8f)
E.set_order(0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1 * 0x1)

PARI/GP

p = 0xc302f41d932a36cda7a3463093d18db78fce476de1a86297
a = Mod(0x6a91174076b1e0e19c39c031fe8685c1cae040e5c69a28ef, p)
b = Mod(0x469a28ef7c28cca3dc721d044f4496bcca7ef4146fbf25c9, p)
E = ellinit([a, b])
E[16][1] = 0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1 * 0x1
G = [Mod(0xc0a0647eaab6a48753b033c56cb0f0900a2f5c4853375fd6, p), Mod(0x14b690866abd5bb88b5f4828c1490002e6773fa2fa299b8f, p)]

JSON

{
  "name": "brainpoolP192r1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.3",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xc302f41d932a36cda7a3463093d18db78fce476de1a86297",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0x6a91174076b1e0e19c39c031fe8685c1cae040e5c69a28ef"
    },
    "b": {
      "raw": "0x469a28ef7c28cca3dc721d044f4496bcca7ef4146fbf25c9"
    }
  },
  "generator": {
    "x": {
      "raw": "0xc0a0647eaab6a48753b033c56cb0f0900a2f5c4853375fd6"
    },
    "y": {
      "raw": "0x14b690866abd5bb88b5f4828c1490002e6773fa2fa299b8f"
    }
  },
  "order": "0xc302f41d932a36cda7a3462f9e9e916b5be8f1029ac4acc1",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "3145146591935622866306370409311868292910840518057952172666",
    "anomalous": false,
    "cm_disc": "19126675935624664971820007577303809627897222624878874449029",
    "conductor": "1",
    "discriminant": "944310369424837272716401339845420116098509061277344316275",
    "embedding_degree": "597708622988270780369375236783629788514982957389979358616",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 6,
        "least": 2,
        "r": 3
      },
      {
        "full": 24,
        "least": 24,
        "r": 5
      },
      {
        "full": 3,
        "least": 3,
        "r": 7
      },
      {
        "full": 120,
        "least": 120,
        "r": 11
      },
      {
        "full": 12,
        "least": 4,
        "r": 13
      },
      {
        "full": 136,
        "least": 8,
        "r": 17
      },
      {
        "full": 171,
        "least": 9,
        "r": 19
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "75885465139255996133178324439"
  }
}