{
  "id": 6046,
  "curve_key": "3429753712:-200860436530144",
  "ainvs": [
    "0",
    "1",
    "0",
    "-71453202",
    "232453539361"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 65.86726287439377,
  "faltings_height": 2.641522907961476,
  "conductor": "28345084",
  "bad_primes": [
    "2",
    "43",
    "223",
    "739"
  ],
  "discriminant": "-113380336",
  "regulator": "242.84693806529205041609386851667594614549086",
  "points": [
    [
      "4858",
      "2661"
    ],
    [
      "5726",
      "105281"
    ],
    [
      "71441682/14641",
      "95443307/1771561"
    ]
  ],
  "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=242, b=-2 in y^2+a*x*y+b*y=x^3 gives y^2+242*x*y-2*y=x^3, with discriminant -113380336. 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 16:30:53",
  "updated_at": "2026-10-28 16:30:53"
}