Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.

Parameters

Sources

• Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis

Characteristics

• j-invariant:
  1020779965905066122071591264944845800437831983089209932185532175247822250850
• Trace of Frobenius:
  27241143818186388543882977165641385921
• Discriminant:
  28723632732102194046035667469577626311807405711506937402182952014350388763647
• Embedding degree:
  5744726546420438809207133493915525262356032913537750202727813807449695662502
• CM-discriminant:
  -114152451011885661692758747567358720426551428089432073707056005693826821775483
• Conductor:
  1

SAGE

p = 0x3f80ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
K = GF(p)
a = K(0x3f80fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc)
b = K(-0x2f72)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0x3f80ffffffffffffffffffffffffffffeb818bea0da375c06fa419c4af8df83f * 0x01)

PARI/GP

p = 0x3f80ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
a = Mod(0x3f80fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc, p)
b = Mod(-0x2f72, p)
E = ellinit([a, b])
E[16][1] = 0x3f80ffffffffffffffffffffffffffffeb818bea0da375c06fa419c4af8df83f * 0x01
\\ No generator defined

JSON

{
  "name": "w-254-mont",
  "desc": "Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.",
  "sources": [
    {
      "name": "Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis",
      "url": "https://eprint.iacr.org/2014/130"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x3f80ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
    "bits": 254
  },
  "params": {
    "a": {
      "raw": "0x3f80fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc"
    },
    "b": {
      "raw": "-0x2f72"
    }
  },
  "order": "0x3f80ffffffffffffffffffffffffffffeb818bea0da375c06fa419c4af8df83f",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-114152451011885661692758747567358720426551428089432073707056005693826821775483",
    "conductor": "1",
    "discriminant": "28723632732102194046035667469577626311807405711506937402182952014350388763647",
    "j_invariant": "1020779965905066122071591264944845800437831983089209932185532175247822250850",
    "embedding_degree": "5744726546420438809207133493915525262356032913537750202727813807449695662502",
    "trace_of_frobenius": "27241143818186388543882977165641385921"
  }
}