Parameters

Characteristics

• OID:
  1.3.36.3.3.2.8.1.1.14
• j-invariant:
  4509057370854421686186036011236846088241121285273238499519398365475754889496855834716692459441995587736488042188935834263974814230487405741844272852058903
• Trace of Frobenius:
  133911538952573548431982907995132016398065354869678696041884562716142492272779
• Discriminant:
  366142109299010382866812622361146894344809310498368746982237761809826581372599425766162889759353387519191323604313390132911397203950040971486611728352565
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  1491493701275038758609433802526525570360434940683059085224099531200009501735569754729830288440587493309575233061671546763849035935647007328892398685924028

SAGE

p = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3
K = GF(p)
a = K(0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f0)
b = K(0x7cbbbcf9441cfab76e1890e46884eae321f70c0bcb4981527897504bec3e36a62bcdfa2304976540f6450085f2dae145c22553b465763689180ea2571867423e)
E = EllipticCurve(K, (a, b))
G = E(0x640ece5c12788717b9c1ba06cbc2a6feba85842458c56dde9db1758d39c0313d82ba51735cdb3ea499aa77a7d6943a64f7a3f25fe26f06b51baa2696fa9035da, 0x5b534bd595f5af0fa2c892376c84ace1bb4e3019b71634c01131159cae03cee9d9932184beef216bd71df2dadf86a627306ecff96dbb8bace198b61e00f8b332)
E.set_order(0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069 * 0x1)

PARI/GP

p = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3
a = Mod(0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f0, p)
b = Mod(0x7cbbbcf9441cfab76e1890e46884eae321f70c0bcb4981527897504bec3e36a62bcdfa2304976540f6450085f2dae145c22553b465763689180ea2571867423e, p)
E = ellinit([a, b])
E[16][1] = 0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069 * 0x1
G = [Mod(0x640ece5c12788717b9c1ba06cbc2a6feba85842458c56dde9db1758d39c0313d82ba51735cdb3ea499aa77a7d6943a64f7a3f25fe26f06b51baa2696fa9035da, p), Mod(0x5b534bd595f5af0fa2c892376c84ace1bb4e3019b71634c01131159cae03cee9d9932184beef216bd71df2dadf86a627306ecff96dbb8bace198b61e00f8b332, p)]

JSON

{
  "name": "brainpoolP512t1",
  "desc": "",
  "oid": "1.3.36.3.3.2.8.1.1.14",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f3",
    "bits": 512
  },
  "params": {
    "a": {
      "raw": "0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca703308717d4d9b009bc66842aecda12ae6a380e62881ff2f2d82c68528aa6056583a48f0"
    },
    "b": {
      "raw": "0x7cbbbcf9441cfab76e1890e46884eae321f70c0bcb4981527897504bec3e36a62bcdfa2304976540f6450085f2dae145c22553b465763689180ea2571867423e"
    }
  },
  "generator": {
    "x": {
      "raw": "0x640ece5c12788717b9c1ba06cbc2a6feba85842458c56dde9db1758d39c0313d82ba51735cdb3ea499aa77a7d6943a64f7a3f25fe26f06b51baa2696fa9035da"
    },
    "y": {
      "raw": "0x5b534bd595f5af0fa2c892376c84ace1bb4e3019b71634c01131159cae03cee9d9932184beef216bd71df2dadf86a627306ecff96dbb8bace198b61e00f8b332"
    }
  },
  "order": "0xaadd9db8dbe9c48b3fd4e6ae33c9fc07cb308db3b3c9d20ed6639cca70330870553e5c414ca92619418661197fac10471db1d381085ddaddb58796829ca90069",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "4509057370854421686186036011236846088241121285273238499519398365475754889496855834716692459441995587736488042188935834263974814230487405741844272852058903",
    "anomalous": false,
    "discriminant": "366142109299010382866812622361146894344809310498368746982237761809826581372599425766162889759353387519191323604313390132911397203950040971486611728352565",
    "embedding_degree": "1491493701275038758609433802526525570360434940683059085224099531200009501735569754729830288440587493309575233061671546763849035935647007328892398685924028",
    "supersingular": false,
    "trace_of_frobenius": "133911538952573548431982907995132016398065354869678696041884562716142492272779"
  }
}