Parameters

Characteristics

• OID:
  1.3.132.0.24
• j-invariant:
  10663224531220005320982145434103390472892057958057683389940
• Trace of Frobenius:
  -123763275178439483174011368593
• Discriminant:
  6227610566229294112017936480812099737256078134172818311188

SAGE

F.<x> = GF(2)[]
K = GF(2^193, name="x", modulus=u^193 +  u^15 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01), 0, 0, K.from_integer(0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814)))
E.set_order(0x01000000000000000000000000c7f34a778f443acc920eba49 * 0x2)
G = E(K.from_integer(0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1), K.from_integer(0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05))

JSON

{
  "name": "sect193r1",
  "desc": "",
  "oid": "1.3.132.0.24",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 193,
    "poly": [
      {
        "power": 193,
        "coeff": "0x01"
      },
      {
        "power": 15,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "degree": 193,
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01"
    },
    "b": {
      "raw": "0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1"
    },
    "y": {
      "raw": "0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05"
    }
  },
  "order": "0x01000000000000000000000000c7f34a778f443acc920eba49",
  "cofactor": "0x2",
  "aliases": [
    "x963/ansit193r1"
  ],
  "characteristics": {
    "discriminant": "6227610566229294112017936480812099737256078134172818311188",
    "j_invariant": "10663224531220005320982145434103390472892057958057683389940",
    "trace_of_frobenius": "-123763275178439483174011368593"
  }
}