Parameters

Sources

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

Characteristics

• j-invariant:
  1255033703828987787697616537237266250094419551325336715616153938849047572
• Trace of Frobenius:
  3
• Discriminant:
  649984036618580650517457639880809241130212612684388740651176129031894476
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1456268479172808959148733486940327264608218463421238003553122264354852868
• CM-discriminant:
  -211
• Conductor:
  166153499473114484112975882535035935

SAGE

p = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007
K = GF(p)
a = K(0x44cfc0f3bc92ec82f818b443b564cf25dee3ebae7902e370f9e80283d3bd)
b = K(0x2ddfd5f7d30c9daca565cd8278eddf6e9497f27450ac97a0a69aac57e27e)
E = EllipticCurve(K, (a, b))
G = E(0xb071579c8cc322dc7fdce378e5b539b4b7580823aba3cfdd6637cbfa0bbb, 0x15d1b75795732b1e2db1efa55cdbb19357e0aa0422cc03b442809339cf02)
E.set_order(0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005 * 0x01)

PARI/GP

p = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007
a = Mod(0x44cfc0f3bc92ec82f818b443b564cf25dee3ebae7902e370f9e80283d3bd, p)
b = Mod(0x2ddfd5f7d30c9daca565cd8278eddf6e9497f27450ac97a0a69aac57e27e, p)
E = ellinit([a, b])
E[16][1] = 0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005 * 0x01
G = [Mod(0xb071579c8cc322dc7fdce378e5b539b4b7580823aba3cfdd6637cbfa0bbb, p), Mod(0x15d1b75795732b1e2db1efa55cdbb19357e0aa0422cc03b442809339cf02, p)]

JSON

{
  "name": "mnt5/3",
  "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": "0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271007",
    "bits": 240
  },
  "params": {
    "a": {
      "raw": "0x44cfc0f3bc92ec82f818b443b564cf25dee3ebae7902e370f9e80283d3bd"
    },
    "b": {
      "raw": "0x2ddfd5f7d30c9daca565cd8278eddf6e9497f27450ac97a0a69aac57e27e"
    }
  },
  "generator": {
    "x": {
      "raw": "0xb071579c8cc322dc7fdce378e5b539b4b7580823aba3cfdd6637cbfa0bbb"
    },
    "y": {
      "raw": "0x15d1b75795732b1e2db1efa55cdbb19357e0aa0422cc03b442809339cf02"
    }
  },
  "order": "0xd2fffffffffffffffffffffffe9058d000000000000000000000a0271005",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "649984036618580650517457639880809241130212612684388740651176129031894476",
    "j_invariant": "1255033703828987787697616537237266250094419551325336715616153938849047572",
    "trace_of_frobenius": "3",
    "embedding_degree": "1456268479172808959148733486940327264608218463421238003553122264354852868",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-211",
    "conductor": "166153499473114484112975882535035935"
  }
}