{
  "id": 228,
  "curve_key": "50629669687232646175504:-11288555295116543539429879836435392",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-1054784785150680128656",
    "13065457517847594395316291335056"
  ],
  "rank_lower_bound": 17,
  "naive_height": 156.8364741443496,
  "faltings_height": 10.930791016522752,
  "conductor": "762280333750526640710523123060225480376357258533234759120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "2673780583403",
    "127364387666511563",
    "65221931972159992355269"
  ],
  "discriminant": "1360395974824539864077627986338200801298862217868752080515916800",
  "regulator": "7177491058583459.51584888066459172079556927610102951940280269290181167717",
  "points": [
    [
      "17260477840",
      "-40992094518804"
    ],
    [
      "17246277940",
      "63064660477104"
    ],
    [
      "24225497616",
      "-1315334066540780"
    ],
    [
      "11406892960",
      "1586780838736236"
    ],
    [
      "284620084",
      "-3572851471915440"
    ],
    [
      "40638644366",
      "-6108611231978970"
    ],
    [
      "20259905326",
      "107585434400730"
    ],
    [
      "15878430446",
      "-566103220644390"
    ],
    [
      "13834761766",
      "1058651718838230"
    ],
    [
      "14208971316",
      "973020615775120"
    ],
    [
      "-25673092112",
      "-4819098757440084"
    ],
    [
      "21213251841",
      "-485848870950080"
    ],
    [
      "-3324637152",
      "4066384915623316"
    ],
    [
      "16892740438",
      "-260467627781334"
    ],
    [
      "27534201573",
      "-2212999545762434"
    ],
    [
      "221094522540",
      "-102895942434903904"
    ],
    [
      "155912503597/4",
      "44664916210304247/8"
    ]
  ],
  "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_u2_v5 with specialization T=4092/1.",
  "created_at": "2026-06-25 23:18:45",
  "updated_at": "2026-07-01 22:34:40"
}