{
  "id": 141,
  "curve_key": "300196990023777109586241:-166444815493197580496764574456504289",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-6254103958828689783047",
    "192644462377949614527629133622271"
  ],
  "rank_lower_bound": 16,
  "naive_height": 162.19994376961367,
  "faltings_height": 11.38894579782904,
  "conductor": "197022936627971949727076998839217404055886430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "4957",
    "662481733",
    "3590490075461",
    "2040263823050317"
  ],
  "discriminant": "-376536091399324797873843080279052128419264348845053873848320000000",
  "regulator": "17919212545940.76402947779221547681853496450696895958880561434176750487",
  "points": [
    [
      "53439808611",
      "-3322744229288306"
    ],
    [
      "-21612040989",
      "-17824518768613106"
    ],
    [
      "186751168611",
      "-74416602330008306"
    ],
    [
      "46440583651",
      "-1536227171551986"
    ],
    [
      "47426885331",
      "1646042061718414"
    ],
    [
      "41564839011",
      "2121899058826894"
    ],
    [
      "46657841601",
      "1553506183449034"
    ],
    [
      "48467974611",
      "-1838227029374306"
    ],
    [
      "48663260835",
      "1881323206446862"
    ],
    [
      "-46310678589",
      "19569252140718094"
    ],
    [
      "-84530314589",
      "-10830706474635506"
    ],
    [
      "46331440071",
      "1529027925038974"
    ],
    [
      "52676761011",
      "3060719801512894"
    ],
    [
      "18056988411",
      "-9252130297002506"
    ],
    [
      "63593508531",
      "-7218393089868146"
    ],
    [
      "27919745211",
      "6308334046772494"
    ]
  ],
  "submitter": "Alexey Pozdnyakov",
  "commentary": "Generated with assistance from OpenAI Codex, based on GPT-5. Method: generalized Mestre/Fermigier quartic-family search, sieving Mestre (u,v) families by Mestre-Nagao score, rescoring survivors, exact-height triaging the best candidates, and certifying top score/height candidates with GP famcert. This hit came from the low-denominator region 1 <= n <= 40, family mestre_um2_vm4, specialization T=6951/10. GP famcert certified rank >= 16. conductor record for rank 16: log N 101.991894 < 107.496352",
  "created_at": "2026-06-24 01:17:09",
  "updated_at": "2026-07-01 22:38:38"
}