{
  "id": 6038,
  "curve_key": "1421970417504:-1695648547564538328",
  "ainvs": [
    "0",
    "0",
    "1",
    "-29624383698",
    "1962556189310808"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 83.9491939309505,
  "faltings_height": 4.0055627731376475,
  "conductor": "1302170715",
  "bad_primes": [
    "3",
    "5",
    "73",
    "229",
    "577"
  ],
  "discriminant": "-1302170715",
  "regulator": "4790.9195744571925700714188630127544921345624",
  "points": [
    [
      "25644336081/258064",
      "-55375047/131096512"
    ],
    [
      "309308835741724/3112635681",
      "-86797479467951/173657057278671"
    ],
    [
      "1730382256778994/17413177681",
      "2574861402159045/2297825513607079"
    ]
  ],
  "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=1092, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+1092*x*y-y=x^3, with discriminant -1302170715. 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 15:44:32",
  "updated_at": "2026-10-28 15:44:32"
}