Parameters

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  29710571568175507457408237575
• Discriminant:
  882718062907666288196217719514349254081211436024346574435
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  392319139070073905864985653114187382750741137407664805213
• Conductor:
  3

SAGE

p = 0x240001B0000948001E60004134005F10005DC0003A800013
K = GF(p)
a = K(0x000000000000000000000000000000000000000000000000)
b = K(0x000000000000000000000000000000000000000000001001)
E = EllipticCurve(K, (a, b))
G = E(0x240001B0000948001E60004134005F10005DC0003A800012, 0x000000000000000000000000000000000000000000000040)
E.set_order(0x240001B0000948001E600040D4005CD0005760003180000D * 0x01)

PARI/GP

p = 0x240001B0000948001E60004134005F10005DC0003A800013
a = Mod(0x000000000000000000000000000000000000000000000000, p)
b = Mod(0x000000000000000000000000000000000000000000001001, p)
E = ellinit([a, b])
E[16][1] = 0x240001B0000948001E600040D4005CD0005760003180000D * 0x01
G = [Mod(0x240001B0000948001E60004134005F10005DC0003A800012, p), Mod(0x000000000000000000000000000000000000000000000040, p)]

JSON

{
  "name": "bn190",
  "desc": "",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x240001B0000948001E60004134005F10005DC0003A800013",
    "bits": 190
  },
  "params": {
    "a": {
      "raw": "0x000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x000000000000000000000000000000000000000000001001"
    }
  },
  "generator": {
    "x": {
      "raw": "0x240001B0000948001E60004134005F10005DC0003A800012"
    },
    "y": {
      "raw": "0x000000000000000000000000000000000000000000000040"
    }
  },
  "order": "0x240001B0000948001E600040D4005CD0005760003180000D",
  "cofactor": "0x01",
  "characteristics": {
    "j_invariant": "0",
    "anomalous": false,
    "cm_disc": "392319139070073905864985653114187382750741137407664805213",
    "conductor": "3",
    "discriminant": "882718062907666288196217719514349254081211436024346574435",
    "embedding_degree": "12",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 6,
        "least": 2,
        "r": 3
      },
      {
        "full": 8,
        "least": 8,
        "r": 5
      },
      {
        "full": 6,
        "least": 2,
        "r": 7
      },
      {
        "full": 6,
        "least": 6,
        "r": 11
      },
      {
        "full": 12,
        "least": 4,
        "r": 13
      },
      {
        "full": 4,
        "least": 4,
        "r": 17
      },
      {
        "full": 18,
        "least": 9,
        "r": 19
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "29710571568175507457408237575"
  }
}