{
  "id": 4312,
  "curve_key": "104605045993:8221352940168715",
  "ainvs": [
    "1",
    "1",
    "0",
    "-2179271791",
    "-9516362821775"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 76.12037288479362,
  "faltings_height": 4.407916145043565,
  "conductor": "293853198970733402778",
  "bad_primes": [
    "2",
    "3",
    "61",
    "73",
    "79",
    "97",
    "109",
    "673",
    "1993",
    "9817"
  ],
  "discriminant": "623275652125933552840414259844",
  "regulator": "617635815.08967756191783748354757447058195491486180902564",
  "points": [
    [
      "-12214",
      "3914987"
    ],
    [
      "-24273/4",
      "14957927/8"
    ],
    [
      "71844",
      "14273153"
    ],
    [
      "131844",
      "44599553"
    ],
    [
      "-261165200/13689",
      "8042049153035/1601613"
    ],
    [
      "-372104/9",
      "85565621/27"
    ],
    [
      "108127051/2116",
      "342438086647/97336"
    ],
    [
      "730158841/14400",
      "5515923501679/1728000"
    ],
    [
      "1071853037/16129",
      "24094949245337/2048383"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "Curve 2-9.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 09:49:45",
  "updated_at": "2026-10-17 09:49:45"
}