Parameters

Characteristics

• OID:
  1.3.132.0.35
• Seed:
  D09E8800291CB85396CC6717393284AAA0DA64BA
• j-invariant:
  3619090631887053412807272747807643016060282478111249168973675223587770705025281286979867546071268566958111997954788345609183745222693618155278831649044785613
• Trace of Frobenius:
  657877501894328237357444332315020117536923257219387276263472201219398408051703
• Discriminant:
  2687853087729004331535582886185403114835754464152651523509230634031161977750238608042000458607319784141115468556368066113806987449553072575343372028907331922

SAGE

p = 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
K = GF(p)
a = K(0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc)
b = K(0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00)
E = EllipticCurve(K, (a, b))
G = E(0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66, 0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650)
E.set_order(0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409 * 0x1)

PARI/GP

p = 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
a = Mod(0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc, p)
b = Mod(0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00, p)
E = ellinit([a, b])
E[16][1] = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409 * 0x1
G = [Mod(0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66, p), Mod(0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650, p)]

JSON

{
  "name": "secp521r1",
  "desc": "",
  "oid": "1.3.132.0.35",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
    "bits": 521
  },
  "params": {
    "a": {
      "raw": "0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc"
    },
    "b": {
      "raw": "0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00"
    }
  },
  "generator": {
    "x": {
      "raw": "0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66"
    },
    "y": {
      "raw": "0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650"
    }
  },
  "order": "0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
  "cofactor": "0x1",
  "aliases": [
    "nist/P-521",
    "x963/ansip521r1"
  ],
  "characteristics": {
    "seed": "D09E8800291CB85396CC6717393284AAA0DA64BA",
    "j_invariant": "3619090631887053412807272747807643016060282478111249168973675223587770705025281286979867546071268566958111997954788345609183745222693618155278831649044785613",
    "discriminant": "2687853087729004331535582886185403114835754464152651523509230634031161977750238608042000458607319784141115468556368066113806987449553072575343372028907331922",
    "trace_of_frobenius": "657877501894328237357444332315020117536923257219387276263472201219398408051703"
  }
}