{
  "id": 146,
  "curve_key": "266689216733149514371666825:-4191183778124329311075024652317330473125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-5556025348607281549409726",
    "4850907150606399626446672370423348348"
  ],
  "rank_lower_bound": 18,
  "naive_height": 182.544378690093,
  "faltings_height": 13.13781303731339,
  "conductor": "9120814589307131223357058040664717870768277440871516003950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "43",
    "59",
    "109",
    "4289",
    "215507435356125127",
    "33984357076304424732533341601"
  ],
  "discriminant": "811199414708319103053032954716768368937184231487647543973012218268927562500",
  "regulator": "15766637859188658.989463949045535958988597456763312195003257509017069237721",
  "points": [
    [
      "1138306568247",
      "-37396477182461549"
    ],
    [
      "3142973901027",
      "-4293677880641280689"
    ],
    [
      "22836036442977",
      "-108566183571808263089"
    ],
    [
      "5819352360516",
      "13022669701398455716"
    ],
    [
      "1083747051522",
      "-320079105741957224"
    ],
    [
      "587537547102",
      "1337666265527601361"
    ],
    [
      "1630066809897",
      "354250759937068651"
    ],
    [
      "1612633529747",
      "291320348627899551"
    ],
    [
      "12987694770903/4",
      "-36696958747221394507/8"
    ],
    [
      "-1913451133473",
      "-2911421483283008939"
    ],
    [
      "4714344382032",
      "9134240722855240396"
    ],
    [
      "720443413816947",
      "-19337374121787475106099"
    ],
    [
      "6113245803303",
      "-14119082368348176203"
    ],
    [
      "135656188487163/4",
      "-1576286240662244845417/8"
    ],
    [
      "85928392099863/4",
      "-791921937724290050467/8"
    ],
    [
      "10939779827704557/16",
      "-1144222024948804078791071/64"
    ],
    [
      "437151064634118/169",
      "-6130650012875911790528/2197"
    ],
    [
      "45869362770434967/3721",
      "9655585436888094099575191/226981"
    ]
  ],
  "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 family mestre_u2_vm4, specialization T=826/9. GP famcert certified rank >= 18. conductor record for rank 18: log N 133.457909 < 138.988198 naive-height record for rank 18: h 182.544379 < 190.774340",
  "created_at": "2026-06-24 03:58:14",
  "updated_at": "2026-07-01 22:31:43"
}