{
  "id": 147,
  "curve_key": "14610038047126711711563601:-56460945334792536314946406246129423705",
  "ainvs": [
    "1",
    "0",
    "0",
    "-304375792648473160657575",
    "65348316359688219048467264095557961"
  ],
  "rank_lower_bound": 18,
  "naive_height": 173.85322502782768,
  "faltings_height": 12.356639211207849,
  "conductor": "21419202627854163602361890682263820949374863109651290731136698",
  "bad_primes": [
    "2",
    "13",
    "41891672862379899773",
    "19665375703497198008963188787543007713701"
  ],
  "discriminant": "-40091900068111500354981590451888913785493616412246049722990279496695808",
  "regulator": "328231786777603894.93250258653942856450752812415634945940058946359937174453",
  "points": [
    [
      "665672967286",
      "397122969151581061"
    ],
    [
      "528305906806",
      "-228032571604209659"
    ],
    [
      "1621064762358",
      "-1957512507166916987"
    ],
    [
      "141813046806",
      "-158227285823597147"
    ],
    [
      "-449951132122",
      "333477709769604789"
    ],
    [
      "-309393665930",
      "-360421436078099579"
    ],
    [
      "360905322078",
      "50063259539241389"
    ],
    [
      "-592171937290",
      "-194770351490693499"
    ],
    [
      "-635714776838",
      "43943567005787149"
    ],
    [
      "-169705070602",
      "-334835632751779451"
    ],
    [
      "942176398838",
      "784180116547849093"
    ],
    [
      "-86690933482",
      "-301800268160975291"
    ],
    [
      "1293065099350",
      "1354177290109513669"
    ],
    [
      "16301299883334/25",
      "-47452911614929710287/125"
    ],
    [
      "-1515067081250/9",
      "9028530617604404087/27"
    ],
    [
      "1623779416726",
      "1962768340928734021"
    ],
    [
      "8394886876764/25",
      "-3961023236839620973/125"
    ],
    [
      "2206741920622934/9025",
      "-63832311566160807668517/857375"
    ]
  ],
  "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=3433/2. GP famcert certified rank >= 18. naive-height record for rank 18: h 173.853225 < 190.774340",
  "created_at": "2026-06-24 03:58:36",
  "updated_at": "2026-07-01 22:31:42"
}