{
  "id": 6035,
  "curve_key": "46753261785:-10109225235997341",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-974026287",
    "11700735677865"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 73.70444958314813,
  "faltings_height": 3.2169083832755323,
  "conductor": "5585814",
  "bad_primes": [
    "2",
    "3",
    "13",
    "73",
    "109"
  ],
  "discriminant": "-100544652",
  "regulator": "622.58784182109980938511716570188108780513994",
  "points": [
    [
      "17620",
      "83615"
    ],
    [
      "318738130/17689",
      "-21196055985/2352637"
    ],
    [
      "13890560455/770884",
      "-6097955788595/676836152"
    ]
  ],
  "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=465, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+465*x*y-y=x^3, with discriminant -100544652. 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 15:29:20",
  "updated_at": "2026-10-28 15:29:20"
}