Parameters

Sources

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

Characteristics

• j-invariant:
  327672737112578556672933546167246593305795867129
• Trace of Frobenius:
  3
• Discriminant:
  416330146701509871347454797378722894990374675389
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  519518160144969382386592375449686021630483366068
• CM-discriminant:
  -91
• Conductor:
  151115727451828644755795

SAGE

p = 0x5affffffffffff4b46081000000059bb1bf600b7
K = GF(p)
a = K(0x07b29491c1a02cd87844f5098d0381f6c45d6523)
b = K(0x41cc630bd66ac817d43358b108ad3d214037993c)
E = EllipticCurve(K, (a, b))
G = E(0x0d76b3e1f1ed76a282fa99575d29ff2e587049e9, 0x36e1557ed145ad409f924420e12f74a900fab054)
E.set_order(0x5affffffffffff4b46081000000059bb1bf600b5 * 0x01)

PARI/GP

p = 0x5affffffffffff4b46081000000059bb1bf600b7
a = Mod(0x07b29491c1a02cd87844f5098d0381f6c45d6523, p)
b = Mod(0x41cc630bd66ac817d43358b108ad3d214037993c, p)
E = ellinit([a, b])
E[16][1] = 0x5affffffffffff4b46081000000059bb1bf600b5 * 0x01
G = [Mod(0x0d76b3e1f1ed76a282fa99575d29ff2e587049e9, p), Mod(0x36e1557ed145ad409f924420e12f74a900fab054, p)]

JSON

{
  "name": "mnt2/2",
  "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": "0x07b29491c1a02cd87844f5098d0381f6c45d6523"
    },
    "b": {
      "raw": "0x41cc630bd66ac817d43358b108ad3d214037993c"
    }
  },
  "generator": {
    "x": {
      "raw": "0x0d76b3e1f1ed76a282fa99575d29ff2e587049e9"
    },
    "y": {
      "raw": "0x36e1557ed145ad409f924420e12f74a900fab054"
    }
  },
  "order": "0x5affffffffffff4b46081000000059bb1bf600b5",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "416330146701509871347454797378722894990374675389",
    "j_invariant": "327672737112578556672933546167246593305795867129",
    "trace_of_frobenius": "3",
    "embedding_degree": "519518160144969382386592375449686021630483366068",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-91",
    "conductor": "151115727451828644755795"
  }
}