Parameters

Sources

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

Characteristics

• j-invariant:
  1124984654526861897351865205551134254199281270688380623003333782861539023
• Trace of Frobenius:
  3
• Discriminant:
  22212718378197970123459632370220319722374785667515184443175879566492100
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1124984654526861897351865205551134254199281270688380623265871195502307020
• CM-discriminant:
  -163
• Conductor:
  166153499473114484112975882535041529

SAGE

p = 0xa2ffffffffffffffffffffffffc298b00000000000000000000005c866cf
K = GF(p)
a = K(0x4be28760aa064734852cb4ff51ef2928a7a3cd75087c35cb1433714f7407)
b = K(0x329704eb1c042f7858c878aa369f70c5c517de4e05a823dcb8224b8a4d5a)
E = EllipticCurve(K, (a, b))
G = E(0x82556d57811807a0d7675674b3d57222cfbf9a2a2a2cd146572d7b67627e, 0x73afacea28dc870baa1d5b0bd4300ddd975e2eefc7c2db508fc2e92a8345)
E.set_order(0xa2ffffffffffffffffffffffffc298b00000000000000000000005c866cd * 0x01)

PARI/GP

p = 0xa2ffffffffffffffffffffffffc298b00000000000000000000005c866cf
a = Mod(0x4be28760aa064734852cb4ff51ef2928a7a3cd75087c35cb1433714f7407, p)
b = Mod(0x329704eb1c042f7858c878aa369f70c5c517de4e05a823dcb8224b8a4d5a, p)
E = ellinit([a, b])
E[16][1] = 0xa2ffffffffffffffffffffffffc298b00000000000000000000005c866cd * 0x01
G = [Mod(0x82556d57811807a0d7675674b3d57222cfbf9a2a2a2cd146572d7b67627e, p), Mod(0x73afacea28dc870baa1d5b0bd4300ddd975e2eefc7c2db508fc2e92a8345, p)]

JSON

{
  "name": "mnt4",
  "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": "0xa2ffffffffffffffffffffffffc298b00000000000000000000005c866cf",
    "bits": 240
  },
  "params": {
    "a": {
      "raw": "0x4be28760aa064734852cb4ff51ef2928a7a3cd75087c35cb1433714f7407"
    },
    "b": {
      "raw": "0x329704eb1c042f7858c878aa369f70c5c517de4e05a823dcb8224b8a4d5a"
    }
  },
  "generator": {
    "x": {
      "raw": "0x82556d57811807a0d7675674b3d57222cfbf9a2a2a2cd146572d7b67627e"
    },
    "y": {
      "raw": "0x73afacea28dc870baa1d5b0bd4300ddd975e2eefc7c2db508fc2e92a8345"
    }
  },
  "order": "0xa2ffffffffffffffffffffffffc298b00000000000000000000005c866cd",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "22212718378197970123459632370220319722374785667515184443175879566492100",
    "j_invariant": "1124984654526861897351865205551134254199281270688380623003333782861539023",
    "trace_of_frobenius": "3",
    "embedding_degree": "1124984654526861897351865205551134254199281270688380623265871195502307020",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-163",
    "conductor": "166153499473114484112975882535041529"
  }
}