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:
  1.3.132.0.29
• Seed:
  004D696E67687561517512D8F03431FCE63B88F4
• j-invariant:
  194900232209907094972416409296981867603
• Trace of Frobenius:
  19023044537425668468
• Discriminant:
  296974453756101405409198998476964181399
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  3866845076846387936543441905764257299
• CM-discriminant:
  340282366762482138430090171110323893666
• Conductor:
  2

SAGE

p = 0xfffffffdffffffffffffffffffffffff
K = GF(p)
a = K(0xd6031998d1b3bbfebf59cc9bbff9aee1)
b = K(0x5eeefca380d02919dc2c6558bb6d8a5d)
E = EllipticCurve(K, (a, b))
G = E(0x7b6aa5d85e572983e6fb32a7cdebc140, 0x27b6916a894d3aee7106fe805fc34b44)
E.set_order(0x3fffffff7fffffffbe0024720613b5a3 * 0x04)

PARI/GP

p = 0xfffffffdffffffffffffffffffffffff
a = Mod(0xd6031998d1b3bbfebf59cc9bbff9aee1, p)
b = Mod(0x5eeefca380d02919dc2c6558bb6d8a5d, p)
E = ellinit([a, b])
E[16][1] = 0x3fffffff7fffffffbe0024720613b5a3 * 0x04
G = [Mod(0x7b6aa5d85e572983e6fb32a7cdebc140, p), Mod(0x27b6916a894d3aee7106fe805fc34b44, p)]

JSON

{
  "name": "secp128r2",
  "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": "1.3.132.0.29",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffdffffffffffffffffffffffff",
    "bits": 128
  },
  "params": {
    "a": {
      "raw": "0xd6031998d1b3bbfebf59cc9bbff9aee1"
    },
    "b": {
      "raw": "0x5eeefca380d02919dc2c6558bb6d8a5d"
    }
  },
  "generator": {
    "x": {
      "raw": "0x7b6aa5d85e572983e6fb32a7cdebc140"
    },
    "y": {
      "raw": "0x27b6916a894d3aee7106fe805fc34b44"
    }
  },
  "order": "0x3fffffff7fffffffbe0024720613b5a3",
  "cofactor": "0x04",
  "characteristics": {
    "seed": "004D696E67687561517512D8F03431FCE63B88F4",
    "j_invariant": "194900232209907094972416409296981867603",
    "anomalous": false,
    "cm_disc": "340282366762482138430090171110323893666",
    "conductor": "2",
    "discriminant": "296974453756101405409198998476964181399",
    "embedding_degree": "3866845076846387936543441905764257299",
    "torsion_degrees": [
      {
        "full": 2,
        "least": 1,
        "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": 12,
        "least": 3,
        "r": 13
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "19023044537425668468"
  }
}