{
  "id": 6034,
  "curve_key": "347892406272:-205195306944432024",
  "ainvs": [
    "0",
    "0",
    "1",
    "-7247758464",
    "237494568222722"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 79.72547727460919,
  "faltings_height": 3.707746221453732,
  "conductor": "1358954739",
  "bad_primes": [
    "3",
    "1549",
    "10831"
  ],
  "discriminant": "-12230592651",
  "regulator": "795.85403819000025054523242646291858262408182",
  "points": [
    [
      "26190",
      "8101846"
    ],
    [
      "49200",
      "18433"
    ],
    [
      "73234520084721/1489960000",
      "-23648928513481/57512456000000"
    ]
  ],
  "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=768, b=-3 in y^2+a*x*y+b*y=x^3 gives y^2+768*x*y-3*y=x^3, with discriminant -12230592651. 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 14:42:48",
  "updated_at": "2026-10-28 14:42:48"
}