Parameters

Characteristics

• OID:
  1.2.250.1.223.101.256.1
• Seed:
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
• j-invariant:
  40896549830710972397896969473453290820546317441961689722588313512802554631657
• Trace of Frobenius:
  -35197163533674495870879651530057169373
• Discriminant:
  36852496142108626283186094975130945312915652343771992238361306471587988304996
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  18242428555282879769611787505122521357667424468567068775512033867954346593872
• CM-discriminant:
  437818285326789114470682900122940512583912595755008627124676173876314146744809
• Conductor:
  1

SAGE

p = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03
K = GF(p)
a = K(0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00)
b = K(0xee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f)
E = EllipticCurve(K, (a, b))
G = E(0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff, 0x6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb)
E.set_order(0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1 * 0x1)

PARI/GP

p = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03
a = Mod(0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00, p)
b = Mod(0xee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f, p)
E = ellinit([a, b])
E[16][1] = 0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1 * 0x1
G = [Mod(0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff, p), Mod(0x6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb, p)]

JSON

{
  "name": "FRP256v1",
  "desc": "",
  "oid": "1.2.250.1.223.101.256.1",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00"
    },
    "b": {
      "raw": "0xee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f"
    }
  },
  "generator": {
    "x": {
      "raw": "0xb6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff"
    },
    "y": {
      "raw": "0x6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb"
    }
  },
  "order": "0xf1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1",
  "cofactor": "0x1",
  "characteristics": {
    "seed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
    "j_invariant": "40896549830710972397896969473453290820546317441961689722588313512802554631657",
    "anomalous": false,
    "cm_disc": "437818285326789114470682900122940512583912595755008627124676173876314146744809",
    "conductor": "1",
    "discriminant": "36852496142108626283186094975130945312915652343771992238361306471587988304996",
    "embedding_degree": "18242428555282879769611787505122521357667424468567068775512033867954346593872",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 8,
        "least": 8,
        "r": 3
      },
      {
        "full": 12,
        "least": 12,
        "r": 5
      },
      {
        "full": 6,
        "least": 2,
        "r": 7
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "-35197163533674495870879651530057169373"
  }
}