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bn222

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

Parameters

NameValue
p0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000067
a0x00000000000000000000000000000000000000000000000000000000
b0x00000000000000000000000000000000000000000000000000000101
G(0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000066, 0x00000000000000000000000000000000000000000000000000000010)
n0x23DC0D7DC02402CDE486F4C00015555156000000496DA00000000061
h0x01

Characteristics

  • j-invariant:
    0
  • Trace of Frobenius:
    1943310227059934816526534243778567
  • Discriminant:
    3776454638595735622662624104352071470606035506175466834584696299191
  • Anomalous:
    false
  • Supersingular:
    false
  • Embedding degree:
    12
  • CM-discriminant:
    1678424283820326943405610713045364882123768329418561201311628394541

SAGE

p = 0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000067
K = GF(p)
a = K(0x00000000000000000000000000000000000000000000000000000000)
b = K(0x00000000000000000000000000000000000000000000000000000101)
E = EllipticCurve(K, (a, b))
G = E(0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000066, 0x00000000000000000000000000000000000000000000000000000010)
E.set_order(0x23DC0D7DC02402CDE486F4C00015555156000000496DA00000000061 * 0x01)

PARI/GP

p = 0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000067
a = Mod(0x00000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x00000000000000000000000000000000000000000000000000000101, p)
E = ellinit([a, b])
E[16][1] = 0x23DC0D7DC02402CDE486F4C00015555156000000496DA00000000061 * 0x01
G = [Mod(0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000066, p), Mod(0x00000000000000000000000000000000000000000000000000000010, p)]

JSON

{
"name": "bn222",
"desc": "",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000067",
"bits": 222
},
"params": {
"a": {
"raw": "0x00000000000000000000000000000000000000000000000000000000"
},
"b": {
"raw": "0x00000000000000000000000000000000000000000000000000000101"
}
},
"generator": {
"x": {
"raw": "0x23DC0D7DC02402CDE486F4C00015B5215C0000004C6CE00000000066"
},
"y": {
"raw": "0x00000000000000000000000000000000000000000000000000000010"
}
},
"order": "0x23DC0D7DC02402CDE486F4C00015555156000000496DA00000000061",
"cofactor": "0x01",
"characteristics": {
"j_invariant": "0",
"anomalous": false,
"cm_disc": "1678424283820326943405610713045364882123768329418561201311628394541",
"discriminant": "3776454638595735622662624104352071470606035506175466834584696299191",
"embedding_degree": "12",
"supersingular": false,
"trace_of_frobenius": "1943310227059934816526534243778567"
}
}

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