Tweedledum pairing friendly curve from https://github.com/daira/tweedle.

Parameters

Sources

• Tweedledum/Tweedledee supporting evidence

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  885929826233106195063767041
• Discriminant:
  28948022309329048855892746252171976963322203655955319056773317069363642095057
• Embedding degree:
  28948022309329048855892746252171976963322203655954433126947083963168578338816
• CM-discriminant:
  -3
• Conductor:
  196462116142286827589390971285842952193

SAGE

p = 0x40000000000000000000000000000000038aa1276c3f59b9a14064e200000001
K = GF(p)
a = K(0x00)
b = K(0x05)
E = EllipticCurve(K, (a, b))
G = E(0x40000000000000000000000000000000038aa1276c3f59b9a14064e200000000, 0x02)
E.set_order(0x40000000000000000000000000000000038aa127696286c9842cafd400000001 * 0x01)

PARI/GP

p = 0x40000000000000000000000000000000038aa1276c3f59b9a14064e200000001
a = Mod(0x00, p)
b = Mod(0x05, p)
E = ellinit([a, b])
E[16][1] = 0x40000000000000000000000000000000038aa127696286c9842cafd400000001 * 0x01
G = [Mod(0x40000000000000000000000000000000038aa1276c3f59b9a14064e200000000, p), Mod(0x02, p)]

JSON

{
  "name": "Tweedledum",
  "desc": "Tweedledum pairing friendly curve from <https://github.com/daira/tweedle>.",
  "sources": [
    {
      "name": "Tweedledum/Tweedledee supporting evidence",
      "url": "https://github.com/daira/tweedle"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x40000000000000000000000000000000038aa1276c3f59b9a14064e200000001",
    "bits": 255
  },
  "params": {
    "a": {
      "raw": "0x00"
    },
    "b": {
      "raw": "0x05"
    }
  },
  "generator": {
    "x": {
      "raw": "0x40000000000000000000000000000000038aa1276c3f59b9a14064e200000000"
    },
    "y": {
      "raw": "0x02"
    }
  },
  "order": "0x40000000000000000000000000000000038aa127696286c9842cafd400000001",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-3",
    "conductor": "196462116142286827589390971285842952193",
    "discriminant": "28948022309329048855892746252171976963322203655955319056773317069363642095057",
    "j_invariant": "0",
    "embedding_degree": "28948022309329048855892746252171976963322203655954433126947083963168578338816",
    "trace_of_frobenius": "885929826233106195063767041"
  }
}