Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.13
• j-invariant:
  4509057370854421686186036011236846088241121285273238499519398365475754889496855834716692459441995587736488042188935834263974814230487405741844272852058903
• Trace of Frobenius:
  133911538952573548431982907995132016398065354869678696041884562716142492272779
• Discriminant:
  7104545390680367735362575245212799391756304950447646185784046656533783808330053676263837968192868620640190094921262822248977297403787578048464541722920343
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1491493701275038758609433802526525570360434940683059085224099531200009501735569754729830288440587493309575233061671546763849035935647007328892398685924028

SAGE

p = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3
K = GF(p)
a = K(0x7830a3318b603b89e2327145ac234cc594cbdd8d3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94ca)
b = K(0x3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94cadc083e67984050b75ebae5dd2809bd638016f723)
E = EllipticCurve(K, (a, b))
G = E(0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822, 0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892)
E.set_order(0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069 * 0x1)

PARI/GP

p = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3
a = Mod(0x7830a3318b603b89e2327145ac234cc594cbdd8d3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94ca, p)
b = Mod(0x3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94cadc083e67984050b75ebae5dd2809bd638016f723, p)
E = ellinit([a, b])
E[16][1] = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069 * 0x1
G = [Mod(0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822, p), Mod(0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892, p)]

JSON

{
  "name": "brainpoolP512r1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.13",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3",
    "bits": 512
  },
  "params": {
    "a": {
      "raw": "0x7830a3318b603b89e2327145ac234cc594cbdd8d3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94ca"
    },
    "b": {
      "raw": "0x3df91610a83441caea9863bc2ded5d5aa8253aa10a2ef1c98b9ac8b57f1117a72bf2c7b9e7c1ac4d77fc94cadc083e67984050b75ebae5dd2809bd638016f723"
    }
  },
  "generator": {
    "x": {
      "raw": "0x81aee4bdd82ed9645a21322e9c4c6a9385ed9f70b5d916c1b43b62eef4d0098eff3b1f78e2d0d48d50d1687b93b97d5f7c6d5047406a5e688b352209bcb9f822"
    },
    "y": {
      "raw": "0x7dde385d566332ecc0eabfa9cf7822fdf209f70024a57b1aa000c55b881f8111b2dcde494a5f485e5bca4bd88a2763aed1ca2b2fa8f0540678cd1e0f3ad80892"
    }
  },
  "order": "0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "4509057370854421686186036011236846088241121285273238499519398365475754889496855834716692459441995587736488042188935834263974814230487405741844272852058903",
    "anomalous": false,
    "discriminant": "7104545390680367735362575245212799391756304950447646185784046656533783808330053676263837968192868620640190094921262822248977297403787578048464541722920343",
    "embedding_degree": "1491493701275038758609433802526525570360434940683059085224099531200009501735569754729830288440587493309575233061671546763849035935647007328892398685924028",
    "supersingular": false,
    "trace_of_frobenius": "133911538952573548431982907995132016398065354869678696041884562716142492272779"
  }
}