{
  "id": 3711,
  "curve_key": "3353238257968827644106609:-6140399373629067890989373173904527497",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-69859130374350575918888",
    "7106943719495552619386843632295147"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 169.41590626489275,
  "faltings_height": 11.491152039269881,
  "conductor": "65902957246370790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "37",
    "53",
    "101",
    "113",
    "127",
    "149"
  ],
  "discriminant": "2269159638517652028241474546319295218162667867820064043171840",
  "regulator": "64736.466076055482767657813583662272375728797564088",
  "points": [
    [
      "152593944685",
      "3113797511961"
    ],
    [
      "-21921722998875/121",
      "156452483647300190171/1331"
    ],
    [
      "3163884318595/36",
      "8763699918162167143/216"
    ],
    [
      "18457879218597/121",
      "48778698207704027/1331"
    ],
    [
      "34394447011561/225",
      "606114969229344571/3375"
    ],
    [
      "80791543011933/529",
      "1038838519202111375/12167"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 2707062/16837 of the universal curve with a 6-torsion point, y^2 + txy + (t+2)y = x^3 (as searched in arXiv:2003.00077, Sec. 13), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:47:51",
  "updated_at": "2026-09-30 01:47:51"
}