Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.7
• j-invariant:
  75626560605944752908522971663649678250473810658385377252202978737957396909999
• Trace of Frobenius:
  300418416528525664980082381967979838673
• Discriminant:
  15036242490247342171513009477805930598983339216081386851174014206346325949410
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  38442478198522672110404873314500824546368765892207264769377759531531768179539
• CM-discriminant:
  307539825588181376883238986516006596371851382387243695149962323398158084952331
• Conductor:
  1

SAGE

p = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377
K = GF(p)
a = K(0x7d5a0975fc2c3057eef67530417affe7fb8055c126dc5c6ce94a4b44f330b5d9)
b = K(0x26dc5c6ce94a4b44f330b5d9bbd77cbf958416295cf7e1ce6bccdc18ff8c07b6)
E = EllipticCurve(K, (a, b))
G = E(0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262, 0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997)
E.set_order(0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7 * 0x1)

PARI/GP

p = 0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377
a = Mod(0x7d5a0975fc2c3057eef67530417affe7fb8055c126dc5c6ce94a4b44f330b5d9, p)
b = Mod(0x26dc5c6ce94a4b44f330b5d9bbd77cbf958416295cf7e1ce6bccdc18ff8c07b6, p)
E = ellinit([a, b])
E[16][1] = 0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7 * 0x1
G = [Mod(0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262, p), Mod(0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997, p)]

JSON

{
  "name": "brainpoolP256r1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.7",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xa9fb57dba1eea9bc3e660a909d838d726e3bf623d52620282013481d1f6e5377",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0x7d5a0975fc2c3057eef67530417affe7fb8055c126dc5c6ce94a4b44f330b5d9"
    },
    "b": {
      "raw": "0x26dc5c6ce94a4b44f330b5d9bbd77cbf958416295cf7e1ce6bccdc18ff8c07b6"
    }
  },
  "generator": {
    "x": {
      "raw": "0x8bd2aeb9cb7e57cb2c4b482ffc81b7afb9de27e1e3bd23c23a4453bd9ace3262"
    },
    "y": {
      "raw": "0x547ef835c3dac4fd97f8461a14611dc9c27745132ded8e545c1d54c72f046997"
    }
  },
  "order": "0xa9fb57dba1eea9bc3e660a909d838d718c397aa3b561a6f7901e0e82974856a7",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "75626560605944752908522971663649678250473810658385377252202978737957396909999",
    "anomalous": false,
    "cm_disc": "307539825588181376883238986516006596371851382387243695149962323398158084952331",
    "conductor": "1",
    "discriminant": "15036242490247342171513009477805930598983339216081386851174014206346325949410",
    "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"
  }
}