{
  "id": 4583,
  "curve_key": "41033862453860323974849897:-192424079621941087258288944743007132981",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-854872134455423416142706",
    "222713055118201087545522356713997636"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 176.92931961357394,
  "faltings_height": 12.76709990135264,
  "conductor": "1372047185460717527629907305167678",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "29",
    "37",
    "43",
    "47",
    "103",
    "109",
    "149",
    "1129",
    "3319",
    "4684736527"
  ],
  "discriminant": "18556066559714424280044604583087760613275847900321647438214691677112055504",
  "regulator": "267362603.628960915115611908344464139548776781123337913937628",
  "points": [
    [
      "-3754462125197/4",
      "3561485377228648793/8"
    ],
    [
      "-2276953286994071/2601",
      "72680948895296538462715/132651"
    ],
    [
      "-369072724580",
      "698534307782544394"
    ],
    [
      "1150136750476",
      "-872302597509939470"
    ],
    [
      "20055809450131",
      "-89723117174792962595"
    ],
    [
      "-1016145573184",
      "205340770101103854"
    ],
    [
      "-727247197796",
      "678073921192172890"
    ],
    [
      "-456880048765",
      "719665581196207744"
    ],
    [
      "-182957940739",
      "610732797357714234"
    ],
    [
      "773911036864",
      "156980600724047086"
    ],
    [
      "-5931409777964804/6889",
      "323696539056315486041582/571787"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-11.ec.\r\n\r\nThe Weierstrass coefficients and eleven rational-point witnesses are reproduced from the original public submission. The source identifies this as an independent construction without specifying further methodological details.\r\n\r\nSubmitted to ICARM to document these improvements and make the curve available to other researchers.",
  "created_at": "2026-10-18 08:12:48",
  "updated_at": "2026-10-18 08:12:48"
}