{
  "id": 4582,
  "curve_key": "2298472540622509081:602018334780590303929046915",
  "ainvs": [
    "1",
    "0",
    "1",
    "-47884844596302273",
    "-696780484060531382943068"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 126.8363293903036,
  "faltings_height": 8.636096015346423,
  "conductor": "1470210055845288515574478669853106",
  "bad_primes": [
    "2",
    "3",
    "19",
    "43",
    "53",
    "71",
    "101",
    "109",
    "193",
    "227",
    "331",
    "997",
    "3391",
    "4339",
    "34033"
  ],
  "discriminant": "6817331735714869117536734578049899026522846195750672",
  "regulator": "84995896596978.473008400051111674161189659311348740527388654478",
  "points": [
    [
      "-185608537",
      "1340519298570"
    ],
    [
      "-105555277",
      "1783765050246"
    ],
    [
      "-86583532",
      "1673413255056"
    ],
    [
      "-21841372",
      "581965292736"
    ],
    [
      "-72806809",
      "-1550326660470"
    ],
    [
      "-119413369",
      "-1821623281362"
    ],
    [
      "315229796",
      "-3941327388645"
    ],
    [
      "264830036",
      "-2279543569317"
    ],
    [
      "13001661356",
      "1482295471059288"
    ],
    [
      "249956380247/529",
      "-110294411004400698/12167"
    ],
    [
      "23411986473629506316/35884103761",
      "-106570641552948007432177008195/6797561659549991"
    ],
    [
      "690463992694511/105625",
      "-18133023607123734059466/34328125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/2-r12-z2low.ec.\r\n\r\nSpecialization u = 10/3, t = 1/8 of the Elkies–Klagsbrun Z/2Z family (arXiv:2003.00077). The original submission describes a rational-parameter census using a height filter, Mestre–Nagao sieving and PARI/GP rank computations.\r\n\r\nSubmitted to ICARM to document these improvements and make the curve available to other researchers.",
  "created_at": "2026-10-18 08:12:21",
  "updated_at": "2026-10-18 08:12:21"
}