{
  "id": 227,
  "curve_key": "148475898081321006759169:-54029095534595783965295888107674497",
  "ainvs": [
    "1",
    "1",
    "1",
    "-3093247876694187640816",
    "62533675385974785566766181200209"
  ],
  "rank_lower_bound": 17,
  "naive_height": 160.06412878638767,
  "faltings_height": 11.283366212963237,
  "conductor": "79882435688106568827071480561070837976769102565133891830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "10780355693401696197985355001494040212789352572892563"
  ],
  "discriminant": "204873677594335180956576449314454322564972911516245035826771353600",
  "regulator": "4198210717650867.87015792172390323128899197641083758790537897585914004614",
  "points": [
    [
      "38378058149",
      "-589021931997195"
    ],
    [
      "164608578773",
      "63352818096521829"
    ],
    [
      "41487998879",
      "2369029083476385"
    ],
    [
      "39304923569",
      "1294228037093685"
    ],
    [
      "23928280001",
      "-1489311095968587"
    ],
    [
      "48788824931",
      "5268011129112945"
    ],
    [
      "51542641763",
      "-6326948724258261"
    ],
    [
      "294670874773",
      "-157282021941860603"
    ],
    [
      "55080221653",
      "7698087202523749"
    ],
    [
      "38320924949",
      "-521149441872795"
    ],
    [
      "-20697282539",
      "-10848457303964795"
    ],
    [
      "42781590599",
      "-2915709540138345"
    ],
    [
      "45550376581",
      "-4018065536875755"
    ],
    [
      "158788250041/9",
      "-99024503808654185/27"
    ],
    [
      "-14288127963",
      "-10188882244057499"
    ],
    [
      "25640408453",
      "279851614094949"
    ],
    [
      "25664045453",
      "-227764996973403"
    ]
  ],
  "submitter": "Alexey Pozdnyakov",
  "commentary": "Generated with assistance from OpenAI Codex, based on GPT-5. Method: Generalized Mestre/Fermigier quartic-family search: Mestre-Nagao stage sieve, high-M rescore, exact-height triage, and conductor analysis. Candidate came from family mestre_u2_v5 with specialization T=2307/1.",
  "created_at": "2026-06-25 23:18:44",
  "updated_at": "2026-07-01 22:34:41"
}