A randomly generated curve. SEC2v1 states 'E was chosen verifiably at random as specified in ANSI X9.62 1 from the seed'.

Parameters

Characteristics

• OID:
  1.3.132.0.28
• Seed:
  000E0D4D696E6768756151750CC03A4473D03679
• j-invariant:
  142488586153168470548238628993886102905
• Trace of Frobenius:
  -8476633335676313877
• Discriminant:
  92269531472977194927251796133478512919
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  170141183381241069221661282790178312330
• CM-discriminant:
  1361129467049928553747860362314397557009
• Conductor:
  1

SAGE

p = 0xfffffffdffffffffffffffffffffffff
K = GF(p)
a = K(0xfffffffdfffffffffffffffffffffffc)
b = K(0xe87579c11079f43dd824993c2cee5ed3)
E = EllipticCurve(K, (a, b))
G = E(0x161ff7528b899b2d0c28607ca52c5b86, 0xcf5ac8395bafeb13c02da292dded7a83)
E.set_order(0xfffffffe0000000075a30d1b9038a115 * 0x01)

PARI/GP

p = 0xfffffffdffffffffffffffffffffffff
a = Mod(0xfffffffdfffffffffffffffffffffffc, p)
b = Mod(0xe87579c11079f43dd824993c2cee5ed3, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffe0000000075a30d1b9038a115 * 0x01
G = [Mod(0x161ff7528b899b2d0c28607ca52c5b86, p), Mod(0xcf5ac8395bafeb13c02da292dded7a83, p)]

JSON

{
  "name": "secp128r1",
  "desc": "A randomly generated curve. [SEC2v1](https://www.secg.org/SEC2-Ver-1.0.pdf) states 'E was chosen verifiably at random as specified in ANSI X9.62 [1] from the seed'.",
  "oid": "1.3.132.0.28",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffdffffffffffffffffffffffff",
    "bits": 128
  },
  "params": {
    "a": {
      "raw": "0xfffffffdfffffffffffffffffffffffc"
    },
    "b": {
      "raw": "0xe87579c11079f43dd824993c2cee5ed3"
    }
  },
  "generator": {
    "x": {
      "raw": "0x161ff7528b899b2d0c28607ca52c5b86"
    },
    "y": {
      "raw": "0xcf5ac8395bafeb13c02da292dded7a83"
    }
  },
  "order": "0xfffffffe0000000075a30d1b9038a115",
  "cofactor": "0x01",
  "characteristics": {
    "seed": "000E0D4D696E6768756151750CC03A4473D03679",
    "j_invariant": "142488586153168470548238628993886102905",
    "anomalous": false,
    "cm_disc": "1361129467049928553747860362314397557009",
    "conductor": "1",
    "discriminant": "92269531472977194927251796133478512919",
    "embedding_degree": "170141183381241069221661282790178312330",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 4,
        "least": 4,
        "r": 3
      },
      {
        "full": 24,
        "least": 24,
        "r": 5
      },
      {
        "full": 6,
        "least": 6,
        "r": 7
      },
      {
        "full": 120,
        "least": 120,
        "r": 11
      },
      {
        "full": 168,
        "least": 168,
        "r": 13
      },
      {
        "full": 8,
        "least": 4,
        "r": 17
      },
      {
        "full": 18,
        "least": 9,
        "r": 19
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "-8476633335676313877"
  }
}