{
  "id": 6044,
  "curve_key": "16983571705:-2213316612718093",
  "ainvs": [
    "1",
    "0",
    "1",
    "-353824411",
    "2561679557130"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 70.66653703041509,
  "faltings_height": 2.9847945149304054,
  "conductor": "23522954",
  "bad_primes": [
    "2",
    "7",
    "13",
    "307",
    "421"
  ],
  "discriminant": "-47045908",
  "regulator": "497.42458280692211117731494668010236905376372",
  "points": [
    [
      "10879",
      "-2010"
    ],
    [
      "13940866105/1283689",
      "-7898225990280/1454419637"
    ],
    [
      "27008054799/2486929",
      "-21297518964230/3921887033"
    ]
  ],
  "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=361, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+361*x*y-y=x^3, with discriminant -47045908. 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 16:21:57",
  "updated_at": "2026-10-28 16:21:57"
}