A Koblitz curve.

Parameters

Characteristics

• OID:
  1.3.132.0.10
• j-invariant:
  0
• Trace of Frobenius:
  432420386565659656852420866390673177327
• Discriminant:
  115792089237316195423570985008687907853269984665640564039457584007908834650495
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  19298681539552699237261830834781317975472927379845817397100860523586360249056
• CM-discriminant:
  2058526030885621251974595289043340584056211192337762651115457400734420735597
• Conductor:
  15

SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
K = GF(p)
a = K(0x0000000000000000000000000000000000000000000000000000000000000000)
b = K(0x0000000000000000000000000000000000000000000000000000000000000007)
E = EllipticCurve(K, (a, b))
G = E(0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798, 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)
E.set_order(0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 * 0x1)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
a = Mod(0x0000000000000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x0000000000000000000000000000000000000000000000000000000000000007, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 * 0x1
G = [Mod(0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798, p), Mod(0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8, p)]

JSON

{
  "name": "secp256k1",
  "desc": "A Koblitz curve.",
  "oid": "1.3.132.0.10",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000007"
    }
  },
  "generator": {
    "x": {
      "raw": "0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"
    },
    "y": {
      "raw": "0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"
    }
  },
  "order": "0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141",
  "cofactor": "0x1",
  "aliases": [
    "x963/ansip256k1"
  ],
  "characteristics": {
    "j_invariant": "0",
    "anomalous": false,
    "cm_disc": "2058526030885621251974595289043340584056211192337762651115457400734420735597",
    "conductor": "15",
    "discriminant": "115792089237316195423570985008687907853269984665640564039457584007908834650495",
    "embedding_degree": "19298681539552699237261830834781317975472927379845817397100860523586360249056",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "432420386565659656852420866390673177327"
  }
}