Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.8
• j-invariant:
  75626560605944752908522971663649678250473810658385377252202978737957396909999
• Trace of Frobenius:
  300418416528525664980082381967979838673
• Discriminant:
  88069733320865891917912206859792533286606565385107642270399326924131494932
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  38442478198522672110404873314500824546368765892207264769377759531531768179539
• CM-discriminant:
  307539825588181376883238986516006596371851382387243695149962323398158084952331
• Conductor:
  1

SAGE

p = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377
K = GF(p)
a = K(0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5374)
b = K(0x662c61c430d84ea4fe66a7733d0b76b7bf93ebc4af2f49256ae58101fee92b04)
E = EllipticCurve(K, (a, b))
G = E(0xa3e8eb3cc1cfe7b7732213b23a656149afa142c47aafbc2b79a191562e1305f4, 0x2d996c823439c56d7f7b22e14644417e69bcb6de39d027001dabe8f35b25c9be)
E.set_order(0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7 * 0x1)

PARI/GP

p = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377
a = Mod(0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5374, p)
b = Mod(0x662c61c430d84ea4fe66a7733d0b76b7bf93ebc4af2f49256ae58101fee92b04, p)
E = ellinit([a, b])
E[16][1] = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7 * 0x1
G = [Mod(0xa3e8eb3cc1cfe7b7732213b23a656149afa142c47aafbc2b79a191562e1305f4, p), Mod(0x2d996c823439c56d7f7b22e14644417e69bcb6de39d027001dabe8f35b25c9be, p)]

JSON

{
  "name": "brainpoolP256t1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.8",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5374"
    },
    "b": {
      "raw": "0x662c61c430d84ea4fe66a7733d0b76b7bf93ebc4af2f49256ae58101fee92b04"
    }
  },
  "generator": {
    "x": {
      "raw": "0xa3e8eb3cc1cfe7b7732213b23a656149afa142c47aafbc2b79a191562e1305f4"
    },
    "y": {
      "raw": "0x2d996c823439c56d7f7b22e14644417e69bcb6de39d027001dabe8f35b25c9be"
    }
  },
  "order": "0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "75626560605944752908522971663649678250473810658385377252202978737957396909999",
    "anomalous": false,
    "cm_disc": "307539825588181376883238986516006596371851382387243695149962323398158084952331",
    "conductor": "1",
    "discriminant": "88069733320865891917912206859792533286606565385107642270399326924131494932",
    "embedding_degree": "38442478198522672110404873314500824546368765892207264769377759531531768179539",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 10,
        "least": 2,
        "r": 5
      },
      {
        "full": 48,
        "least": 48,
        "r": 7
      },
      {
        "full": 10,
        "least": 10,
        "r": 11
      },
      {
        "full": 12,
        "least": 3,
        "r": 13
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "300418416528525664980082381967979838673"
  }
}