{
  "id": 5787,
  "curve_key": "0:31440792535903944",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-36389806175815"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 75.97376514007793,
  "faltings_height": 4.388803004131456,
  "conductor": "141467779688813072909649",
  "bad_primes": [
    "3",
    "43",
    "2689",
    "1084297"
  ],
  "discriminant": "-572062173197773818148340969187",
  "regulator": "160444540.18062893491809986016064303890268696870624849909",
  "points": [
    [
      "33205",
      "470210"
    ],
    [
      "39775",
      "5151335"
    ],
    [
      "246691",
      "122377892"
    ],
    [
      "851925",
      "786301789"
    ],
    [
      "948709/25",
      "534128802/125"
    ],
    [
      "4551249/100",
      "7608163693/1000"
    ],
    [
      "3413125/9",
      "6303523303/27"
    ],
    [
      "4640259/25",
      "9967220348/125"
    ],
    [
      "6445749/25",
      "16347395057/125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization at t=-234/95 of a generic rank-four Mordell family generated from the Burkhardt parametrization, using construction parameters (-9,-1,0).\r\n\r\nThe specialization was selected by the common 328-prime Mestre–Nagao sieve in a coordinated search across multiple Burkhardt families and the rank-five quadratic base-change family.\r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [9,9].",
  "created_at": "2026-10-25 08:38:04",
  "updated_at": "2026-10-25 08:38:04"
}