Parameters

Sources

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

Characteristics

• j-invariant:
  15215793501150681155687505726634711188936782904
• Trace of Frobenius:
  3
• Discriminant:
  210597358905446859227534646357086406264047168945
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  793549717144513671927050677226939834588042230468
• CM-discriminant:
  -139
• Conductor:
  151115727451828644749125

SAGE

p = 0x8afffffffffffeeb0fa77000000089f0dd49fac7
K = GF(p)
a = K(0x6d01fd0a017c62075ae999977379867e07f2a6d4)
b = K(0x7701535c00fd965341d38bba4cfbdcf9a4651825)
E = EllipticCurve(K, (a, b))
G = E(0x1781998103c3ca14ea76b9d3a700a53e1c784789, 0x53352dde04447c25c9bb332a3c7634d3b8801f34)
E.set_order(0x8afffffffffffeeb0fa77000000089f0dd49fac5 * 0x01)

PARI/GP

p = 0x8afffffffffffeeb0fa77000000089f0dd49fac7
a = Mod(0x6d01fd0a017c62075ae999977379867e07f2a6d4, p)
b = Mod(0x7701535c00fd965341d38bba4cfbdcf9a4651825, p)
E = ellinit([a, b])
E[16][1] = 0x8afffffffffffeeb0fa77000000089f0dd49fac5 * 0x01
G = [Mod(0x1781998103c3ca14ea76b9d3a700a53e1c784789, p), Mod(0x53352dde04447c25c9bb332a3c7634d3b8801f34, p)]

JSON

{
  "name": "mnt3/1",
  "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": "0x8afffffffffffeeb0fa77000000089f0dd49fac7",
    "bits": 160
  },
  "params": {
    "a": {
      "raw": "0x6d01fd0a017c62075ae999977379867e07f2a6d4"
    },
    "b": {
      "raw": "0x7701535c00fd965341d38bba4cfbdcf9a4651825"
    }
  },
  "generator": {
    "x": {
      "raw": "0x1781998103c3ca14ea76b9d3a700a53e1c784789"
    },
    "y": {
      "raw": "0x53352dde04447c25c9bb332a3c7634d3b8801f34"
    }
  },
  "order": "0x8afffffffffffeeb0fa77000000089f0dd49fac5",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "210597358905446859227534646357086406264047168945",
    "j_invariant": "15215793501150681155687505726634711188936782904",
    "trace_of_frobenius": "3",
    "embedding_degree": "793549717144513671927050677226939834588042230468",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-139",
    "conductor": "151115727451828644749125"
  }
}