{
  "id": 226,
  "curve_key": "2559591262338637286657802227947681:-131846891815534571140347404460393717853020072247921",
  "ainvs": [
    "1",
    "0",
    "0",
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    "152600569230942786227963554343099291511940660100"
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  "rank_lower_bound": 20,
  "naive_height": 230.81145160519077,
  "faltings_height": 17.12490323263689,
  "conductor": "282182911611488014589765703157855796043317619561544915217487973922307930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "31",
    "41",
    "59",
    "79",
    "1615673",
    "140389069210932330034578246587156827594757780759118714191"
  ],
  "discriminant": "-355568117955757642974912655755100242442938536081550074372306129807997878195940027796106400000000",
  "regulator": "22741880954418501814.3623903478549341506058195963051390323906246906003515483700",
  "points": [
    [
      "618601125946370",
      "346194302434275472478840"
    ],
    [
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    ],
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    ],
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      "5722894198425740",
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    ],
    [
      "-6015123623406730",
      "-505686134502279456010810"
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      "-913586879332288",
      "447833570226927052727006"
    ],
    [
      "3467158396446920",
      "-96924402816950500267210"
    ],
    [
      "-2962025209897180",
      "533443925142244344432890"
    ],
    [
      "-1020997989620680",
      "453851050081375324404290"
    ],
    [
      "6555760311182919080/2209",
      "-14859538369702735477983935330/103823"
    ],
    [
      "35422287391675744/9",
      "1640631393230902228935254/27"
    ],
    [
      "1647630816630975820/361",
      "-449530896105195331951787690/6859"
    ],
    [
      "479223846427162851980/113569",
      "1996522496958091344388813918370/38272753"
    ],
    [
      "417628515448521851180/94249",
      "1666221552406370616415079717270/28934443"
    ],
    [
      "80652470616459665420/351649",
      "78130442711385740206728677920930/208527857"
    ]
  ],
  "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 sextuple_C_m138_138_162_m60_m90_m12 with specialization T=10167/350.",
  "created_at": "2026-06-25 23:18:43",
  "updated_at": "2026-07-01 22:29:42"
}