Parameters

Sources

• New explicit conditions of elliptic curve traces for FR-reduction

Characteristics

• j-invariant:
  908761003790427908077548955758380356675829025646511
• Trace of Frobenius:
  -52213820118540299389901413
• Discriminant:
  519081282363855507291976255149499325173130091108552
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  3
• CM-discriminant:
  -19
• Conductor:
  6915889423298038776451801

SAGE

p = 0x26dccacc5041939206cf2b7dec50950e3c9fa4827af
K = GF(p)
a = K(0x22ffbb20cc052993fa27dc507800b624c650e4ff3d2)
b = K(0x1c7be6fa8da953b5624efc72406af7fa77499803d08)
E = EllipticCurve(K, (a, b))
G = E(0x25a3ae778f7ef6586abae5acde21e54b6c64edf33d0, 0x05b4ace33aa53c670ce35535d6c273698a182da557d)
E.set_order(0x0000a60fd646ad409b3312c3b23ba64e082ad7b354d * 0x3be9)

PARI/GP

p = 0x26dccacc5041939206cf2b7dec50950e3c9fa4827af
a = Mod(0x22ffbb20cc052993fa27dc507800b624c650e4ff3d2, p)
b = Mod(0x1c7be6fa8da953b5624efc72406af7fa77499803d08, p)
E = ellinit([a, b])
E[16][1] = 0x0000a60fd646ad409b3312c3b23ba64e082ad7b354d * 0x3be9
G = [Mod(0x25a3ae778f7ef6586abae5acde21e54b6c64edf33d0, p), Mod(0x05b4ace33aa53c670ce35535d6c273698a182da557d, p)]

JSON

{
  "name": "mnt1",
  "desc": "",
  "sources": [
    {
      "name": "New explicit conditions of elliptic curve traces for FR-reduction",
      "url": "https://dspace.jaist.ac.jp/dspace/bitstream/10119/4432/1/73-48.pdf"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x26dccacc5041939206cf2b7dec50950e3c9fa4827af",
    "bits": 170
  },
  "params": {
    "a": {
      "raw": "0x22ffbb20cc052993fa27dc507800b624c650e4ff3d2"
    },
    "b": {
      "raw": "0x1c7be6fa8da953b5624efc72406af7fa77499803d08"
    }
  },
  "generator": {
    "x": {
      "raw": "0x25a3ae778f7ef6586abae5acde21e54b6c64edf33d0"
    },
    "y": {
      "raw": "0x05b4ace33aa53c670ce35535d6c273698a182da557d"
    }
  },
  "order": "0x0000a60fd646ad409b3312c3b23ba64e082ad7b354d",
  "cofactor": "0x3be9",
  "characteristics": {
    "discriminant": "519081282363855507291976255149499325173130091108552",
    "j_invariant": "908761003790427908077548955758380356675829025646511",
    "trace_of_frobenius": "-52213820118540299389901413",
    "embedding_degree": "3",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-19",
    "conductor": "6915889423298038776451801"
  }
}