Parameters

Sources

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

Characteristics

• j-invariant:
  191845423032390825713658829282439417965614485182
• Trace of Frobenius:
  3
• Discriminant:
  502795212314952730723914620087437088076350616414
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  519518160144969382386592375449686021630483366068
• CM-discriminant:
  -91
• Conductor:
  151115727451828644755795

SAGE

p = 0x5affffffffffff4b46081000000059bb1bf600b7
K = GF(p)
a = K(0x3dd24a7e5c0bdfaccc215e22760469c73ee9d879)
b = K(0x478c31a992b294e19f6e4416f958646dddede5e3)
E = EllipticCurve(K, (a, b))
G = E(0x2725af3d7dea98cb9242ac6ddb9bd89bdcf38898, 0x480b4184ed2c50c0230b4c73ca939c1b6b7f1103)
E.set_order(0x5affffffffffff4b46081000000059bb1bf600b5 * 0x01)

PARI/GP

p = 0x5affffffffffff4b46081000000059bb1bf600b7
a = Mod(0x3dd24a7e5c0bdfaccc215e22760469c73ee9d879, p)
b = Mod(0x478c31a992b294e19f6e4416f958646dddede5e3, p)
E = ellinit([a, b])
E[16][1] = 0x5affffffffffff4b46081000000059bb1bf600b5 * 0x01
G = [Mod(0x2725af3d7dea98cb9242ac6ddb9bd89bdcf38898, p), Mod(0x480b4184ed2c50c0230b4c73ca939c1b6b7f1103, p)]

JSON

{
  "name": "mnt2/1",
  "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": "0x5affffffffffff4b46081000000059bb1bf600b7",
    "bits": 159
  },
  "params": {
    "a": {
      "raw": "0x3dd24a7e5c0bdfaccc215e22760469c73ee9d879"
    },
    "b": {
      "raw": "0x478c31a992b294e19f6e4416f958646dddede5e3"
    }
  },
  "generator": {
    "x": {
      "raw": "0x2725af3d7dea98cb9242ac6ddb9bd89bdcf38898"
    },
    "y": {
      "raw": "0x480b4184ed2c50c0230b4c73ca939c1b6b7f1103"
    }
  },
  "order": "0x5affffffffffff4b46081000000059bb1bf600b5",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "502795212314952730723914620087437088076350616414",
    "j_invariant": "191845423032390825713658829282439417965614485182",
    "trace_of_frobenius": "3",
    "embedding_degree": "519518160144969382386592375449686021630483366068",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-91",
    "conductor": "151115727451828644755795"
  }
}