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:
  1.3.132.0.7
• Seed:
  002757A1114D696E6768756151755316C05E0BD4
• j-invariant:
  1815128745141690948653052996943564
• Trace of Frobenius:
  72213667414400864
• Discriminant:
  3350974381310990100142288157262754
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  370973768757809558322577571595630
• CM-discriminant:
  494631691677079417114575713327579
• Conductor:
  6

SAGE

p = 0xdb7c2abf62e35e668076bead208b
K = GF(p)
a = K(0x6127c24c05f38a0aaaf65c0ef02c)
b = K(0x51def1815db5ed74fcc34c85d709)
E = EllipticCurve(K, (a, b))
G = E(0x4ba30ab5e892b4e1649dd0928643, 0xadcd46f5882e3747def36e956e97)
E.set_order(0x36df0aafd8b8d7597ca10520d04b * 0x04)

PARI/GP

p = 0xdb7c2abf62e35e668076bead208b
a = Mod(0x6127c24c05f38a0aaaf65c0ef02c, p)
b = Mod(0x51def1815db5ed74fcc34c85d709, p)
E = ellinit([a, b])
E[16][1] = 0x36df0aafd8b8d7597ca10520d04b * 0x04
G = [Mod(0x4ba30ab5e892b4e1649dd0928643, p), Mod(0xadcd46f5882e3747def36e956e97, p)]

JSON

{
  "name": "secp112r2",
  "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": "1.3.132.0.7",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xdb7c2abf62e35e668076bead208b",
    "bits": 112
  },
  "params": {
    "a": {
      "raw": "0x6127c24c05f38a0aaaf65c0ef02c"
    },
    "b": {
      "raw": "0x51def1815db5ed74fcc34c85d709"
    }
  },
  "generator": {
    "x": {
      "raw": "0x4ba30ab5e892b4e1649dd0928643"
    },
    "y": {
      "raw": "0xadcd46f5882e3747def36e956e97"
    }
  },
  "order": "0x36df0aafd8b8d7597ca10520d04b",
  "cofactor": "0x04",
  "characteristics": {
    "seed": "002757A1114D696E6768756151755316C05E0BD4",
    "j_invariant": "1815128745141690948653052996943564",
    "anomalous": false,
    "cm_disc": "494631691677079417114575713327579",
    "conductor": "6",
    "discriminant": "3350974381310990100142288157262754",
    "embedding_degree": "370973768757809558322577571595630",
    "torsion_degrees": [
      {
        "full": 1,
        "least": 1,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 24,
        "least": 24,
        "r": 5
      },
      {
        "full": 6,
        "least": 3,
        "r": 7
      },
      {
        "full": 10,
        "least": 5,
        "r": 11
      },
      {
        "full": 12,
        "least": 3,
        "r": 13
      },
      {
        "full": 288,
        "least": 288,
        "r": 17
      },
      {
        "full": 360,
        "least": 360,
        "r": 19
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "72213667414400864"
  }
}