{
  "id": 4315,
  "curve_key": "27242582795810368:-2294719080842176481692160",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-567553808246049",
    "2655925051270455158049"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 113.53067306396945,
  "faltings_height": 7.511015565109976,
  "conductor": "7751841093349428163776",
  "bad_primes": [
    "2",
    "3",
    "41",
    "73",
    "79",
    "311",
    "337",
    "953",
    "1193",
    "1433"
  ],
  "discriminant": "8653109808461883529988557689980524859315257344",
  "regulator": "3980874.3394949963683710649200908981580004614199222398327",
  "points": [
    [
      "24450193",
      "58272991680"
    ],
    [
      "-3395193831/169",
      "169463419567200/2197"
    ],
    [
      "15675845/4",
      "-177429119459/8"
    ],
    [
      "62019099/25",
      "4442734772532/125"
    ],
    [
      "-25538893",
      "22209436780"
    ],
    [
      "-22258143",
      "65279242080"
    ],
    [
      "4442751",
      "-14903555400"
    ],
    [
      "-24425824",
      "44112779585"
    ],
    [
      "1991093641/9",
      "88340255736128/27"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "Curve 2x2-9.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 09:50:05",
  "updated_at": "2026-10-17 09:50:05"
}