{
  "id": 6037,
  "curve_key": "443364232320:-295216740795728088",
  "ainvs": [
    "0",
    "0",
    "1",
    "-9236754840",
    "341686042587648"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 80.45297239208335,
  "faltings_height": 3.7354804592506134,
  "conductor": "60370947",
  "bad_primes": [
    "3",
    "7",
    "13",
    "24571"
  ],
  "discriminant": "-543338523",
  "regulator": "3789.1954957229719488339469642645014008029486",
  "points": [
    [
      "4075094298/73441",
      "-9950391/19902511"
    ],
    [
      "149787029436/2699449",
      "-2206969523/4435194707"
    ],
    [
      "11339741415942/483252289",
      "124733516409998977528/10623335069087"
    ]
  ],
  "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=816, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+816*x*y-y=x^3, with discriminant -543338523. 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 15:34:58",
  "updated_at": "2026-10-28 15:34:58"
}