{
  "id": 6081,
  "curve_key": "205546813110608851953:-108895731738626639742329811976425",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-4282225273137684416",
    "126036726550406944908943925706"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 147.5358872493457,
  "faltings_height": 10.352412280735095,
  "conductor": "5126661320120532183815901",
  "bad_primes": [
    "3",
    "7",
    "11",
    "37",
    "67",
    "73",
    "181",
    "397",
    "619",
    "5113",
    "179749"
  ],
  "discriminant": "-6857405174986517490508887687232491385700057838363709500206991",
  "regulator": "21364557.331725510364748301236664310842245324729187550944",
  "points": [
    [
      "-3534417573/4",
      "-2874776619045231/8"
    ],
    [
      "13486626584/49",
      "121210032838761210/343"
    ],
    [
      "-4330494862",
      "-251732430197682"
    ],
    [
      "-3361414501/4",
      "-2873788360621815/8"
    ],
    [
      "-2035564771/16",
      "-22769920934179125/64"
    ],
    [
      "131965178679011/255025",
      "45343345104505522429194/128787625"
    ],
    [
      "46414863876",
      "9996008833864445"
    ],
    [
      "166790271282227/5476",
      "2153877828887456488257/405224"
    ],
    [
      "-264581223159/64",
      "138417048587655145/512"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original search by mpjunior92 (2026), public Yukon elliptic-rank challenge submission 5efdc131-d52e-4b2c-9962-c0b912aa9de8. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/07e2abcc754fd889214af458aeaeb016a2004705/submission/board/4-9.ec . The source used a Mestre-Nagao sieve in the Z/4 Kubert family y^2+x*y-t*y=x^3-t*x^2, with t=u/(D*s^2), (D,s,u)=(3,29711,-2980125361). The nine supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-9 F_5 reduction matrix at ten good primes.",
  "created_at": "2026-10-29 00:44:26",
  "updated_at": "2026-10-29 00:44:26"
}