{
  "id": 233,
  "curve_key": "2258866244939094301443024001:-107387626477141067042781088591229752045249",
  "ainvs": [
    "1",
    "0",
    "0",
    "-47059713436231131280063000",
    "124291234348538980027099166608538874432"
  ],
  "rank_lower_bound": 18,
  "naive_height": 188.9545271849907,
  "faltings_height": 13.474276471831853,
  "conductor": "70641518626311939848441607050541661411730955138276481056543606910",
  "bad_primes": [
    "2",
    "5",
    "17",
    "37",
    "2021179",
    "81005178314881",
    "21895530395507809193",
    "3132826558949676690397"
  ],
  "discriminant": "-3639993566490641216689747626786054555892020902459466267407640882904268800000",
  "regulator": "536817729199543216.84665489380964481059698918907148197929007350386929801579",
  "points": [
    [
      "3239722194224",
      "2415430462344812008"
    ],
    [
      "4499331922864",
      "-1907457031091338392"
    ],
    [
      "3810007955424",
      "-547760266366600392"
    ],
    [
      "3801947170944",
      "573657108993519768"
    ],
    [
      "4147838533344",
      "675939614911732968"
    ],
    [
      "2114906977904",
      "-5850124186730281752"
    ],
    [
      "3404042813824",
      "1882105246884763368"
    ],
    [
      "3609942938544",
      "1204989598722206568"
    ],
    [
      "-7870624775696",
      "2668538857551716648"
    ],
    [
      "30495110821168/9",
      "52200598495644293240/27"
    ],
    [
      "-7193257748656",
      "-9518581173018943032"
    ],
    [
      "10392518468734",
      "-27525637468970450962"
    ],
    [
      "-2527343490552",
      "15069307033302071976"
    ],
    [
      "32676952036364",
      "-182971116416499646472"
    ],
    [
      "-53350585659884/9",
      "-376989394300296149464/27"
    ],
    [
      "249957736105436/49",
      "-1413152923399194615756/343"
    ],
    [
      "23070911278207024/5041",
      "782238092196844207958488/357911"
    ],
    [
      "62220901060271384/7921",
      "10905936898001708604261312/704969"
    ]
  ],
  "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=2623/2.",
  "created_at": "2026-06-25 23:18:49",
  "updated_at": "2026-07-01 22:32:40"
}