{
  "id": 224,
  "curve_key": "320307201103246053866773886521:-180903144453772783632334526461612615679043181",
  "ainvs": [
    "1",
    "0",
    "1",
    "-6673066689650959455557789303",
    "209378639414088313855940823602467379072006"
  ],
  "rank_lower_bound": 18,
  "naive_height": 203.81723414871612,
  "faltings_height": 14.78565705941443,
  "conductor": "572909165125068318062716813219644563458478178791019281490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "29",
    "510907",
    "5615780176703",
    "4413530848208303762736531936829"
  ],
  "discriminant": "79001812652238926310614069141452885179698753918710242185753213892099337491708562500",
  "regulator": "4448647520751208.6688351763983694041782506910401027616687954510865258321494",
  "points": [
    [
      "52648439943435",
      "63135542408283779122"
    ],
    [
      "152427780121155",
      "-1653408591206197043978"
    ],
    [
      "33382358374155",
      "154326358334583163522"
    ],
    [
      "39388005269550",
      "87447073241685904477"
    ],
    [
      "295951840628325",
      "4914890668196834574952"
    ],
    [
      "50025489363555",
      "-27321818658715172978"
    ],
    [
      "154944573237195/4",
      "759491082898156748051/8"
    ],
    [
      "-78057807129435",
      "504634277034685447912"
    ],
    [
      "39508640005905",
      "-86053348519378572728"
    ],
    [
      "-71995604329495",
      "562699303600646341272"
    ],
    [
      "89282248783980",
      "-570341705230530251603"
    ],
    [
      "-49554040294920",
      "646816080171094290397"
    ],
    [
      "93798472814837",
      "-639303212109997850622"
    ],
    [
      "36963847321485",
      "114982967705704135642"
    ],
    [
      "548034406500745/9",
      "-4583878846330509251656/27"
    ],
    [
      "199544434564695/4",
      "201286633741255673801/8"
    ],
    [
      "44390697022770",
      "25098478885753929757"
    ],
    [
      "3862239457538245/144",
      "385208152479162663358691/1728"
    ]
  ],
  "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 sextuple_A_m498_m216_m6_414_552_m246 with specialization T=966/145.",
  "created_at": "2026-06-25 23:18:40",
  "updated_at": "2026-07-01 22:33:40"
}