{
  "id": 6045,
  "curve_key": "4294973440:-281475580690648",
  "ainvs": [
    "0",
    "1",
    "1",
    "-89478613",
    "325752095891"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 66.5421336252861,
  "faltings_height": 2.6711626428130364,
  "conductor": "16777243",
  "bad_primes": [
    "7",
    "37",
    "211",
    "307"
  ],
  "discriminant": "-16777243",
  "regulator": "688.59411535093601220648224181225343069015372",
  "points": [
    [
      "5445",
      "2047"
    ],
    [
      "2296327/81",
      "3306696607/729"
    ],
    [
      "10252999/1849",
      "858594933/79507"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The specialization a=256, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+256*x*y-y=x^3, with discriminant -16777243. The displayed equation is its global minimal model. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/3Z.",
  "created_at": "2026-10-28 16:25:07",
  "updated_at": "2026-10-28 16:25:07"
}