{
  "id": 5851,
  "curve_key": "0:-103527203396472",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "119823152079"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 64.54171105769498,
  "faltings_height": 3.436131830599544,
  "conductor": "2067492639485818598152401",
  "bad_primes": [
    "3",
    "239",
    "2005408403"
  ],
  "discriminant": "-6202477918457455794457203",
  "regulator": "912282525630.40436073514725685109345167564487545131098788",
  "points": [
    [
      "-119823150439/24304900",
      "14498601465559/119823157000"
    ],
    [
      "-9593508007/58767556",
      "155943868489230487/450512084296"
    ],
    [
      "6127501805137/6423701904",
      "178860758520955595399/514846860201792"
    ],
    [
      "3274671722561/473497600",
      "6916356918002867809/10303307776000"
    ],
    [
      "359937202915529/42894552100",
      "7489218010235274864167/8883890685431000"
    ],
    [
      "19674138218561/1524121600",
      "89663400211875078559/59501707264000"
    ],
    [
      "75768797478977/3729789184",
      "664228069954286083681/227785685045248"
    ],
    [
      "80286539522561/3876307600",
      "724223825031926137441/241338911176000"
    ],
    [
      "10179182501728489/5890911494400",
      "5054726501086774825905013/14297949106288128000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt parametrization (-2,-9,10), generic rank-four sextic; specialization t=-64/109. The 3-isogenous partner has global minimal equation y^2+y=x^3+119823152079. PARI/GP 2.17.4 returned rank bounds [9,9].",
  "created_at": "2026-10-25 12:06:11",
  "updated_at": "2026-10-25 12:06:11"
}