{
  "id": 4314,
  "curve_key": "121996527354688:137239163528077411840",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-2541594319889",
    "-158840777255686671"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 97.30504108785256,
  "faltings_height": 6.176360682210483,
  "conductor": "16123341663260539584",
  "bad_primes": [
    "2",
    "3",
    "31",
    "47",
    "59",
    "97",
    "131",
    "193",
    "379",
    "1051"
  ],
  "discriminant": "1039848585560932572112814629035323572224",
  "regulator": "213012.717321805152279611834950697361240593483331040837",
  "points": [
    [
      "36965605",
      "224538992672"
    ],
    [
      "-642944",
      "1099765145"
    ],
    [
      "2146485",
      "-2067697008"
    ],
    [
      "8500431",
      "-24340395720"
    ],
    [
      "2776015",
      "3765413512"
    ],
    [
      "-79654883/81",
      "859336807760/729"
    ],
    [
      "-826061",
      "-1173450316"
    ],
    [
      "-345251",
      "823100096"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "Curve 2x2-8.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 09:49:59",
  "updated_at": "2026-10-17 09:49:59"
}