Parameters

Characteristics

• OID:
  1.2.840.10045.3.1.4
• Seed:
  E43BB460F0B80CC0C0B075798E948060F8321B7D
• j-invariant:
  535250236995642411828071436390811255989556058215461384191615097928272770
• Trace of Frobenius:
  506926255561332610517105435906892533
• Discriminant:
  304850035712828017768890753913370930082366291391142991141919368057646026
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  441711766194596082395824375180154442403775170845813876137672712351403653
• CM-discriminant:
  3533694129556768659166595001441235540750980133450508840652698006531906823
• Conductor:
  1

SAGE

p = 0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff
K = GF(p)
a = K(0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc)
b = K(0x6b016c3bdcf18941d0d654921475ca71a9db2fb27d1d37796185c2942c0a)
E = EllipticCurve(K, (a, b))
G = E(0x0ffa963cdca8816ccc33b8642bedf905c3d358573d3f27fbbd3b3cb9aaaf, 0x7debe8e4e90a5dae6e4054ca530ba04654b36818ce226b39fccb7b02f1ae)
E.set_order(0x7fffffffffffffffffffffff7fffff9e5e9a9f5d9071fbd1522688909d0b * 0x1)

PARI/GP

p = 0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff
a = Mod(0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc, p)
b = Mod(0x6b016c3bdcf18941d0d654921475ca71a9db2fb27d1d37796185c2942c0a, p)
E = ellinit([a, b])
E[16][1] = 0x7fffffffffffffffffffffff7fffff9e5e9a9f5d9071fbd1522688909d0b * 0x1
G = [Mod(0x0ffa963cdca8816ccc33b8642bedf905c3d358573d3f27fbbd3b3cb9aaaf, p), Mod(0x7debe8e4e90a5dae6e4054ca530ba04654b36818ce226b39fccb7b02f1ae, p)]

JSON

{
  "name": "prime239v1",
  "desc": "",
  "oid": "1.2.840.10045.3.1.4",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff",
    "bits": 239
  },
  "params": {
    "a": {
      "raw": "0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc"
    },
    "b": {
      "raw": "0x6b016c3bdcf18941d0d654921475ca71a9db2fb27d1d37796185c2942c0a"
    }
  },
  "generator": {
    "x": {
      "raw": "0x0ffa963cdca8816ccc33b8642bedf905c3d358573d3f27fbbd3b3cb9aaaf"
    },
    "y": {
      "raw": "0x7debe8e4e90a5dae6e4054ca530ba04654b36818ce226b39fccb7b02f1ae"
    }
  },
  "order": "0x7fffffffffffffffffffffff7fffff9e5e9a9f5d9071fbd1522688909d0b",
  "cofactor": "0x1",
  "characteristics": {
    "seed": "E43BB460F0B80CC0C0B075798E948060F8321B7D",
    "j_invariant": "535250236995642411828071436390811255989556058215461384191615097928272770",
    "anomalous": false,
    "cm_disc": "3533694129556768659166595001441235540750980133450508840652698006531906823",
    "conductor": "1",
    "discriminant": "304850035712828017768890753913370930082366291391142991141919368057646026",
    "embedding_degree": "441711766194596082395824375180154442403775170845813876137672712351403653",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 12,
        "least": 12,
        "r": 5
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "506926255561332610517105435906892533"
  }
}