Parameters

Characteristics

• OID:
  1.3.132.0.37
• Seed:
  4099B5A457F9D69F79213D094C4BCD4D4262210B
• j-invariant:
  754296572979130966367055702570030140076184810784727299570664029563208238737796673624760610953546729716274009429339787708937
• Trace of Frobenius:
  -6059503967182126918765909026644927652236777310526686418445029
• Discriminant:
  86886261634090707672817770640384425264505829479043641824438658614111870471004564988634410809058207142318571212147935892575
• Anomalous:
  false
• Supersingular:
  false

SAGE

F.<x> = GF(2)[]
K = GF(2^409, name="x", modulus= x^409 +  x^87 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f)))
E.set_order(0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 * 0x2)
G = E(K.fetch_int(0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7), K.fetch_int(0x061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706))

JSON

{
  "name": "B-409",
  "desc": "",
  "oid": "1.3.132.0.37",
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 409,
    "degree": 409,
    "poly": [
      {
        "coeff": "0x01",
        "power": 409
      },
      {
        "coeff": "0x01",
        "power": 87
      },
      {
        "coeff": "0x01",
        "power": 0
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
    },
    "b": {
      "raw": "0x021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f"
    }
  },
  "generator": {
    "x": {
      "raw": "0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7"
    },
    "y": {
      "raw": "0x061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706"
    }
  },
  "order": "0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173",
  "cofactor": "0x2",
  "aliases": [
    "secg/sect409r1",
    "x963/ansit409r1"
  ],
  "characteristics": {
    "seed": "4099B5A457F9D69F79213D094C4BCD4D4262210B",
    "j_invariant": "754296572979130966367055702570030140076184810784727299570664029563208238737796673624760610953546729716274009429339787708937",
    "anomalous": false,
    "discriminant": "86886261634090707672817770640384425264505829479043641824438658614111870471004564988634410809058207142318571212147935892575",
    "supersingular": false,
    "trace_of_frobenius": "-6059503967182126918765909026644927652236777310526686418445029"
  }
}