{
  "id": 225,
  "curve_key": "3596661509551646823919413851761825:-215622822992734274035136509381123478909285626560625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-74930448115659308831654455245038",
    "249563452537886885000166950293580142396024130692"
  ],
  "rank_lower_bound": 19,
  "naive_height": 231.79594237663446,
  "faltings_height": 17.053369800115544,
  "conductor": "305612822977927350087196447812113421419402448463094784488568526950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "37",
    "79",
    "89",
    "6379",
    "28166397753511",
    "17930509179380017127220936003343570961"
  ],
  "discriminant": "19165526853195419552478026879498587507276138078291075987245289519588640497575159258293376000000",
  "regulator": "315606972157921062.9287695173038203469728749809356091846689042492693943318539",
  "points": [
    [
      "4882261436067532",
      "10455925384379314803634"
    ],
    [
      "5710070459686252",
      "-88778475080120654768126"
    ],
    [
      "5439993856112332",
      "54137910929405459176834"
    ],
    [
      "4838847837782332",
      "16892856695505555928834"
    ],
    [
      "4909045600971652",
      "-5312630013962056985126"
    ],
    [
      "3784167745652668",
      "-142137498393290391417470"
    ],
    [
      "4343791276627132",
      "-77731268535751116304766"
    ],
    [
      "9639568465898602",
      "-650374750837561993346576"
    ],
    [
      "5081960163093772",
      "4269076187506464793714"
    ],
    [
      "1760155168566532",
      "-350895220399651061347166"
    ],
    [
      "7231883051682652",
      "-293093259063868129124126"
    ],
    [
      "4907638739041852",
      "5653244447855662364674"
    ],
    [
      "20904343537780483/4",
      "212447116156674922899167/8"
    ],
    [
      "9283304033644872",
      "-594973946534384517013386"
    ],
    [
      "328199221517367772",
      "187956238503253577989464514"
    ],
    [
      "4615861527249346",
      "-45180147467781491555720"
    ],
    [
      "5156388008664772",
      "-17110583905139451344486"
    ],
    [
      "5460212511620152",
      "56724109510237623938374"
    ],
    [
      "-187591819551050534312/18769",
      "17143338594991268980322143922/2571353"
    ]
  ],
  "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_u3_vm1 with specialization T=15619/18.",
  "created_at": "2026-06-25 23:18:42",
  "updated_at": "2026-07-01 22:31:40"
}