Pallas curve from the Pasta curves.

Parameters

Sources

• The Pasta Curves for Halo 2 and Beyond

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  -86663725065984043395317759
• Discriminant:
  28948022309329048855892746252171976963363056481941560715954676764349967619537
• Embedding degree:
  1809251394333065553493296640760748560210191030121352961229983921774585184256
• CM-discriminant:
  -3
• Conductor:
  196462116142286827589391630752301449217

SAGE

p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
K = GF(p)
a = K(0x00)
b = K(0x05)
E = EllipticCurve(K, (a, b))
G = E(0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000, 0x02)
E.set_order(0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001 * 0x01)

PARI/GP

p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
a = Mod(0x00, p)
b = Mod(0x05, p)
E = ellinit([a, b])
E[16][1] = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001 * 0x01
G = [Mod(0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000, p), Mod(0x02, p)]

JSON

{
  "name": "Pallas",
  "desc": "Pallas curve from the [Pasta curves](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/).",
  "sources": [
    {
      "name": "The Pasta Curves for Halo 2 and Beyond",
      "url": "https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001",
    "bits": 255
  },
  "params": {
    "a": {
      "raw": "0x00"
    },
    "b": {
      "raw": "0x05"
    }
  },
  "generator": {
    "x": {
      "raw": "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000"
    },
    "y": {
      "raw": "0x02"
    }
  },
  "order": "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-3",
    "conductor": "196462116142286827589391630752301449217",
    "discriminant": "28948022309329048855892746252171976963363056481941560715954676764349967619537",
    "j_invariant": "0",
    "embedding_degree": "1809251394333065553493296640760748560210191030121352961229983921774585184256",
    "trace_of_frobenius": "-86663725065984043395317759"
  }
}