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prime239v2

239-bit prime field Weierstrass curve.
y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0x7fffffffffffffffffffffff7fffffffffff8000000000007fffffffffff
a0x7fffffffffffffffffffffff7fffffffffff8000000000007ffffffffffc
b0x617fab6832576cbbfed50d99f0249c3fee58b94ba0038c7ae84c8c832f2c
G(0x38af09d98727705120c921bb5e9e26296a3cdcf2f35757a0eafd87b830e7, 0x5b0125e4dbea0ec7206da0fc01d9b081329fb555de6ef460237dff8be4ba)
n0x7fffffffffffffffffffffff800000cfa7e8594377d414c03821bc582063
h0x1

Characteristics

  • OID:
    1.2.840.10045.3.1.5
  • Seed:
    0E8B4011604095303CA3B8099982BE09FCB9AE616
  • 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": "0E8B4011604095303CA3B8099982BE09FCB9AE616",
"j_invariant": "845456799438304440285632276028937020105084947748076550483955832603378212",
"anomalous": false,
"cm_disc": "3533694129556768659166595001441235542336117449305874943525118314280394847",
"discriminant": "369528448271621828801750954737572264864367402255299013074552698823670735",
"embedding_degree": "21033893628314099161705922627626402056968753751118901313042041248840365",
"supersingular": false,
"trace_of_frobenius": "-1078211060294033492355314871841595491"
}
}

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