{
  "id": 223,
  "curve_key": "663709995877578012490154121:-17238768115980871498390390175127575397669",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-13827291580782875260211544",
    "19952277912018354390476665828916413300"
  ],
  "rank_lower_bound": 18,
  "naive_height": 185.2959588689216,
  "faltings_height": 13.297374883854571,
  "conductor": "461823608144041018516298274615425366200955693996006396490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "23",
    "37",
    "71",
    "83",
    "210790277",
    "21964674471223643707048498855910313431"
  ],
  "discriminant": "-2779860892166611369042972272150233658744639167770630104181815185350095802500",
  "regulator": "6193872058172542.0698850916042087258173155583103051269994944405161556910590",
  "points": [
    [
      "1227784678841",
      "2196854315198111267"
    ],
    [
      "6134826146759/4",
      "12271431754018974331/8"
    ],
    [
      "1775940598451",
      "998540014077880622"
    ],
    [
      "2345352798959",
      "650718085190954954"
    ],
    [
      "4720531864626",
      "-7737554084669710148"
    ],
    [
      "2058765048281",
      "-459606069645467293"
    ],
    [
      "2652716024666",
      "-1392590093046860308"
    ],
    [
      "1995845950091",
      "552619012550347142"
    ],
    [
      "4472914545539/4",
      "19412943032333863261/8"
    ],
    [
      "-2782573437314/9",
      "132816334947716409844/27"
    ],
    [
      "-4188336217449",
      "2095988457729532402"
    ],
    [
      "39452428375626",
      "-246742606709672325398"
    ],
    [
      "811017706145096/361",
      "3267442518430273060958/6859"
    ],
    [
      "4617508820362619/2209",
      "-44333795825549236071734/103823"
    ],
    [
      "-55963938077416/49",
      "2007499556130315331706/343"
    ],
    [
      "2216745075624",
      "440102525237020394"
    ],
    [
      "48407221607609/64",
      "-1613127844760372797391/512"
    ],
    [
      "61640729874550751/27556",
      "-2120352425314049635526503/4574296"
    ]
  ],
  "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, conductor analysis, and GP famcert certification. Candidate came from family mestre_u4_vm1 with specialization T=20424/65. The same curve also appeared in the fixed sextuple_C model as T=10212/65.",
  "created_at": "2026-06-25 23:18:39",
  "updated_at": "2026-07-01 22:32:40"
}