Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.1
• j-invariant:
  387367055434500543477184371239969891945180101787
• Trace of Frobenius:
  519972310379544251229703
• Discriminant:
  845365293605815390445478703156256339281515926196
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  444099199480014958275695012943393788070980856152
• CM-discriminant:
  592132265973353277700926857248628510609391551437
• Conductor:
  3

SAGE

p = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f
K = GF(p)
a = K(0x340e7be2a280eb74e2be61bada745d97e8f7c300)
b = K(0x1e589a8595423412134faa2dbdec95c8d8675e58)
E = EllipticCurve(K, (a, b))
G = E(0xbed5af16ea3f6a4f62938c4631eb5af7bdbcdbc3, 0x1667cb477a1a8ec338f94741669c976316da6321)
E.set_order(0xe95e4a5f737059dc60df5991d45029409e60fc09 * 0x1)

PARI/GP

p = 0xe95e4a5f737059dc60dfc7ad95b3d8139515620f
a = Mod(0x340e7be2a280eb74e2be61bada745d97e8f7c300, p)
b = Mod(0x1e589a8595423412134faa2dbdec95c8d8675e58, p)
E = ellinit([a, b])
E[16][1] = 0xe95e4a5f737059dc60df5991d45029409e60fc09 * 0x1
G = [Mod(0xbed5af16ea3f6a4f62938c4631eb5af7bdbcdbc3, p), Mod(0x1667cb477a1a8ec338f94741669c976316da6321, p)]

JSON

{
  "name": "brainpoolP160r1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.1",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xe95e4a5f737059dc60dfc7ad95b3d8139515620f",
    "bits": 160
  },
  "params": {
    "a": {
      "raw": "0x340e7be2a280eb74e2be61bada745d97e8f7c300"
    },
    "b": {
      "raw": "0x1e589a8595423412134faa2dbdec95c8d8675e58"
    }
  },
  "generator": {
    "x": {
      "raw": "0xbed5af16ea3f6a4f62938c4631eb5af7bdbcdbc3"
    },
    "y": {
      "raw": "0x1667cb477a1a8ec338f94741669c976316da6321"
    }
  },
  "order": "0xe95e4a5f737059dc60df5991d45029409e60fc09",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "387367055434500543477184371239969891945180101787",
    "anomalous": false,
    "cm_disc": "592132265973353277700926857248628510609391551437",
    "conductor": "3",
    "discriminant": "845365293605815390445478703156256339281515926196",
    "embedding_degree": "444099199480014958275695012943393788070980856152",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 6,
        "least": 2,
        "r": 3
      },
      {
        "full": 12,
        "least": 12,
        "r": 5
      },
      {
        "full": 8,
        "least": 8,
        "r": 7
      },
      {
        "full": 55,
        "least": 5,
        "r": 11
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "519972310379544251229703"
  }
}