Parameters

Characteristics

• OID:
  1.2.840.10045.3.1.5
• Seed:
  E8B4011604095303CA3B8099982BE09FCB9AE616
• j-invariant:
  845456799438304440285632276028937020105084947748076550483955832603378212
• Trace of Frobenius:
  -1078211060294033492355314871841595491
• Discriminant:
  369528448271621828801750954737572264864367402255299013074552698823670735
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  21033893628314099161705922627626402056968753751118901313042041248840365
• CM-discriminant:
  3533694129556768659166595001441235542336117449305874943525118314280394847

SAGE

p = 0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff
K = GF(p)
a = K(0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc)
b = K(0x617fab6832576cbbfed50d99f0249c3fee58b94ba0038c7ae84c8c832f2c)
E = EllipticCurve(K, (a, b))
G = E(0x38af09d98727705120c921bb5e9e26296a3cdcf2f35757a0eafd87b830e7, 0x5b0125e4dbea0ec7206da0fc01d9b081329fb555de6ef460237dff8be4ba)
E.set_order(0x7fffffffffffffffffffffff800000cfa7e8594377d414c03821bc582063 * 0x1)

PARI/GP

p = 0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff
a = Mod(0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc, p)
b = Mod(0x617fab6832576cbbfed50d99f0249c3fee58b94ba0038c7ae84c8c832f2c, p)
E = ellinit([a, b])
E[16][1] = 0x7fffffffffffffffffffffff800000cfa7e8594377d414c03821bc582063 * 0x1
G = [Mod(0x38af09d98727705120c921bb5e9e26296a3cdcf2f35757a0eafd87b830e7, p), Mod(0x5b0125e4dbea0ec7206da0fc01d9b081329fb555de6ef460237dff8be4ba, p)]

JSON

{
  "name": "prime239v2",
  "desc": "",
  "oid": "1.2.840.10045.3.1.5",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff",
    "bits": 239
  },
  "params": {
    "a": {
      "raw": "0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc"
    },
    "b": {
      "raw": "0x617fab6832576cbbfed50d99f0249c3fee58b94ba0038c7ae84c8c832f2c"
    }
  },
  "generator": {
    "x": {
      "raw": "0x38af09d98727705120c921bb5e9e26296a3cdcf2f35757a0eafd87b830e7"
    },
    "y": {
      "raw": "0x5b0125e4dbea0ec7206da0fc01d9b081329fb555de6ef460237dff8be4ba"
    }
  },
  "order": "0x7fffffffffffffffffffffff800000cfa7e8594377d414c03821bc582063",
  "cofactor": "0x1",
  "characteristics": {
    "seed": "E8B4011604095303CA3B8099982BE09FCB9AE616",
    "j_invariant": "845456799438304440285632276028937020105084947748076550483955832603378212",
    "anomalous": false,
    "cm_disc": "3533694129556768659166595001441235542336117449305874943525118314280394847",
    "discriminant": "369528448271621828801750954737572264864367402255299013074552698823670735",
    "embedding_degree": "21033893628314099161705922627626402056968753751118901313042041248840365",
    "supersingular": false,
    "trace_of_frobenius": "-1078211060294033492355314871841595491"
  }
}