{
  "id": 6043,
  "curve_key": "559840671385:-418886794113617341",
  "ainvs": [
    "1",
    "0",
    "1",
    "-11663347321",
    "484821706426632"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 81.1527541944285,
  "faltings_height": 3.7894654028708263,
  "conductor": "323607326",
  "bad_primes": [
    "2",
    "7",
    "31",
    "97",
    "7687"
  ],
  "discriminant": "-647214652",
  "regulator": "1685.3292089388922916731005693232947009547439",
  "points": [
    [
      "4579184223/73441",
      "-619423540192/19902511"
    ],
    [
      "11907299365/190969",
      "-2601776011012/83453453"
    ],
    [
      "54044010477/866761",
      "-25048207735956/806954491"
    ]
  ],
  "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=865, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+865*x*y-y=x^3, with discriminant -647214652. 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 16:06:34",
  "updated_at": "2026-10-28 16:06:34"
}