Parameters

Characteristics

• OID:
  1.2.840.10045.3.1.7
• Seed:
  C49D360886E704936A6678E1139D26B7819F7E90
• j-invariant:
  7958909377132088453074743217357398615041065282494610304372115906626967530147
• Trace of Frobenius:
  89188191154553853111372247798585809583
• Discriminant:
  47064476442213300654454205837611899485069387829947879813735601543372794627813
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  38597363070118749587565815649802524509998985074711920114140753020356170681456
• CM-discriminant:
  51463150760158332783421087533070032680028376163334078103224794776407756178469
• Conductor:
  3

SAGE

p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
K = GF(p)
a = K(0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc)
b = K(0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b)
E = EllipticCurve(K, (a, b))
G = E(0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296, 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5)
E.set_order(0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 * 0x1)

PARI/GP

p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
a = Mod(0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc, p)
b = Mod(0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b, p)
E = ellinit([a, b])
E[16][1] = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 * 0x1
G = [Mod(0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296, p), Mod(0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5, p)]

JSON

{
  "name": "prime256v1",
  "desc": "",
  "oid": "1.2.840.10045.3.1.7",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc"
    },
    "b": {
      "raw": "0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b"
    }
  },
  "generator": {
    "x": {
      "raw": "0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296"
    },
    "y": {
      "raw": "0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"
    }
  },
  "order": "0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
  "cofactor": "0x1",
  "aliases": [
    "secg/secp256r1",
    "nist/P-256"
  ],
  "characteristics": {
    "seed": "C49D360886E704936A6678E1139D26B7819F7E90",
    "j_invariant": "7958909377132088453074743217357398615041065282494610304372115906626967530147",
    "anomalous": false,
    "cm_disc": "51463150760158332783421087533070032680028376163334078103224794776407756178469",
    "conductor": "3",
    "discriminant": "47064476442213300654454205837611899485069387829947879813735601543372794627813",
    "embedding_degree": "38597363070118749587565815649802524509998985074711920114140753020356170681456",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 6,
        "least": 2,
        "r": 3
      },
      {
        "full": 10,
        "least": 2,
        "r": 5
      },
      {
        "full": 16,
        "least": 16,
        "r": 7
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "89188191154553853111372247798585809583"
  }
}