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:
  463573502898485009444670675691079657538117640338338636735686841150835857012423508060857644038055
• Trace of Frobenius:
  -1085868569802514034757079818015930522073462377917
• Discriminant:
  190509007027072986168162856643838550056120230552635469912461975898349170573680140826632463202616
• Embedding degree:
  139800024587753519065746686962916734183420710196489425520964926676890448707163939628912379967284
• CM-discriminant:
  -24583513908120940535393951773433057494153140751760772520791113373580804392885557750143467820707
• Conductor:
  15

SAGE

p = 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3408b3
K = GF(p)
a = K(0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3408b0)
b = K(0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d3695a9e13641146433fbcc939dce249b40a4)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xc90fdaa22168c234c4c6628b80dc1cd129024e09489bd44fda941042cccc7286009777663bb29671 * 0x01)

PARI/GP

p = 0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3408b3
a = Mod(0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3408b0, p)
b = Mod(0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d3695a9e13641146433fbcc939dce249b40a4, p)
E = ellinit([a, b])
E[16][1] = 0xc90fdaa22168c234c4c6628b80dc1cd129024e09489bd44fda941042cccc7286009777663bb29671 * 0x01
\\ No generator defined

JSON

{
  "name": "ssc-320",
  "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": "0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3408b3",
    "bits": 320
  },
  "params": {
    "a": {
      "raw": "0xc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3408b0"
    },
    "b": {
      "raw": "0xadf85458a2bb4a9aafdc5620273d3cf1d8b9c583ce2d3695a9e13641146433fbcc939dce249b40a4"
    }
  },
  "order": "0xc90fdaa22168c234c4c6628b80dc1cd129024e09489bd44fda941042cccc7286009777663bb29671",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-24583513908120940535393951773433057494153140751760772520791113373580804392885557750143467820707",
    "conductor": "15",
    "discriminant": "190509007027072986168162856643838550056120230552635469912461975898349170573680140826632463202616",
    "j_invariant": "463573502898485009444670675691079657538117640338338636735686841150835857012423508060857644038055",
    "embedding_degree": "139800024587753519065746686962916734183420710196489425520964926676890448707163939628912379967284",
    "trace_of_frobenius": "-1085868569802514034757079818015930522073462377917"
  }
}