{
  "id": 231,
  "curve_key": "113112631658713962479617:-38911056875304869346936499385745409",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2356513159556540884992",
    "45035945457332407869731977363456"
  ],
  "rank_lower_bound": 17,
  "naive_height": 159.29317303495907,
  "faltings_height": 11.175283713126262,
  "conductor": "90822486465985344845462123297288403822069848710579842463634",
  "bad_primes": [
    "2",
    "13",
    "863",
    "31787682271043383",
    "915104046386062103",
    "139148940743185753507"
  ],
  "discriminant": "-38688926074726301138649337130672103413740602433127643612028665856",
  "regulator": "28452934182224966.6012110193994401286027763716771254315599232725266211317",
  "points": [
    [
      "5248336256",
      "-5728242982433280"
    ],
    [
      "27508940752",
      "1013855318237440"
    ],
    [
      "23878844464",
      "-1543006612856576"
    ],
    [
      "19737266304",
      "-2492731442864768"
    ],
    [
      "18373533504",
      "-2818010805775168"
    ],
    [
      "92182935072",
      "24721361145021440"
    ],
    [
      "32273096144",
      "-1611878798589648"
    ],
    [
      "30975335294",
      "-1327459810236596"
    ],
    [
      "21214458350",
      "-2142773068047284"
    ],
    [
      "64610326912",
      "-12747436122575360"
    ],
    [
      "26832062936",
      "1060098553036264"
    ],
    [
      "-37518610240",
      "-8979742835342336"
    ],
    [
      "-53256582608",
      "4414330307269840"
    ],
    [
      "-46520921028",
      "-7347269609014412"
    ],
    [
      "1465391525200/49",
      "392432565204690688/343"
    ],
    [
      "531387441448/9",
      "285394583350887880/27"
    ],
    [
      "255616230159/4",
      "99731229782086477/8"
    ]
  ],
  "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, and conductor analysis. Candidate came from family mestre_um2_vm4 with specialization T=79/2.",
  "created_at": "2026-06-25 23:18:48",
  "updated_at": "2026-07-01 22:34:41"
}