A prime order curve from MIRACL: https://github.com/miracl/MIRACL/blob/master/docs/miracl-explained/miracl-standard-curves.md. Has no generator specified.

Parameters

Sources

• MIRACL Standard Curves

Characteristics

• j-invariant:
  174206690758115926887583152500483745004945383683506628698
• Trace of Frobenius:
  -68374409827948938044418153103
• Discriminant:
  1909360066132393619878989026804308935096519596163838912163
• Embedding degree:
  4930024174431634640599033341125441632693811654341940586402
• CM-discriminant:
  -15045036778406218234967275420770217256389969312108541204587
• Conductor:
  1

SAGE

p = 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cd13
K = GF(p)
a = K(0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cd10)
b = K(0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d36a6)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xc90fdaa22168c234c4c6628c5dca19490dd3e6fd7979a7a3 * 0x01)

PARI/GP

p = 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cd13
a = Mod(0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cd10, p)
b = Mod(0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d36a6, p)
E = ellinit([a, b])
E[16][1] = 0xc90fdaa22168c234c4c6628c5dca19490dd3e6fd7979a7a3 * 0x01
\\ No generator defined

JSON

{
  "name": "ssc-192",
  "desc": "A prime order curve from MIRACL: https://github.com/miracl/MIRACL/blob/master/docs/miracl-explained/miracl-standard-curves.md. Has no generator specified.",
  "sources": [
    {
      "name": "MIRACL Standard Curves",
      "url": "https://github.com/miracl/MIRACL/blob/master/docs/miracl-explained/miracl-standard-curves.md"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cd13",
    "bits": 192
  },
  "params": {
    "a": {
      "raw": "0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cd10"
    },
    "b": {
      "raw": "0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d36a6"
    }
  },
  "order": "0xc90fdaa22168c234c4c6628c5dca19490dd3e6fd7979a7a3",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-15045036778406218234967275420770217256389969312108541204587",
    "conductor": "1",
    "discriminant": "1909360066132393619878989026804308935096519596163838912163",
    "j_invariant": "174206690758115926887583152500483745004945383683506628698",
    "embedding_degree": "4930024174431634640599033341125441632693811654341940586402",
    "trace_of_frobenius": "-68374409827948938044418153103"
  }
}