{
  "id": 4319,
  "curve_key": "-40163438400253967:-355261341305936180672224489",
  "ainvs": [
    "1",
    "0",
    "0",
    "836738300005291",
    "411182108062709882259960"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 122.26979184636618,
  "faltings_height": 8.246962933500287,
  "conductor": "975919424884519423407",
  "bad_primes": [
    "3",
    "11",
    "19",
    "31",
    "37",
    "73",
    "79",
    "127",
    "397",
    "733",
    "6367"
  ],
  "discriminant": "-73076046493421968572293293979344183203490123933503",
  "regulator": "494976.202804998748747868148756259627374256316115655449",
  "points": [
    [
      "12747577",
      "-651097753277"
    ],
    [
      "459152577",
      "-9879218339925"
    ],
    [
      "16934105512/49",
      "-2222329858425524/343"
    ],
    [
      "480681024877/1681",
      "337855627491279983/68921"
    ],
    [
      "79326565",
      "-988339350065"
    ],
    [
      "-66867173",
      "237212736700"
    ],
    [
      "3970342843/484",
      "6889122144113629/10648"
    ],
    [
      "188832536365/841",
      "-84202931177354965/24389"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "Curve 4-8.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 09:50:21",
  "updated_at": "2026-10-17 09:50:21"
}