{
  "id": 277,
  "curve_key": "29090204352:-4570432820084736",
  "ainvs": [
    "0",
    "0",
    "0",
    "-606045924",
    "5289852801024"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "naive_height": 72.28100200274513,
  "faltings_height": 3.9853475132874348,
  "conductor": "28428075513538468416",
  "bad_primes": [
    "2",
    "3",
    "11",
    "1216681",
    "335245441"
  ],
  "discriminant": "2157660911429827456151752704",
  "regulator": "4975.3262359149538714498786181623068386819786827935",
  "points": [
    [
      "0",
      "2299968"
    ],
    [
      "24618",
      "2299968"
    ],
    [
      "-17424",
      "3249576"
    ],
    [
      "17358",
      "-8712"
    ],
    [
      "-2112",
      "-2561328"
    ],
    [
      "-15675",
      "3307293"
    ]
  ],
  "submitter": "Daksh Shami",
  "commentary": "Rank >= 6. Found during a preliminary search among rational specializations of the classical one-parameter family y^2 = x^3 - u^2*x + 1, at u = 373/264. The six displayed rational points were certified independent modulo torsion by the ICARM exact 2-descent verifier (descent matrix rank 6), establishing rank E(Q) >= 6. Candidate search and the computational verification workflow were carried out with assistance from OpenAI Codex using GPT-5.6 Sol, together with exact computations in SageMath.\r\n",
  "created_at": "2026-08-21 19:52:52",
  "updated_at": "2026-08-21 19:52:52"
}