{
  "id": 5585,
  "curve_key": "0:737415116565444072",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-853489718247042"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 82.28385476063627,
  "faltings_height": 4.914643805844651,
  "conductor": "6422206327230105208457479480347",
  "bad_primes": [
    "3",
    "7",
    "69672630060983"
  ],
  "discriminant": "-314688110034275155214416494537003",
  "regulator": "712152600065.339881260184878103204424225167968586779112935344",
  "points": [
    [
      "95484",
      "4129946"
    ],
    [
      "125244",
      "33333093"
    ],
    [
      "375858",
      "228568770"
    ],
    [
      "1225722",
      "1356710877"
    ],
    [
      "7755174",
      "21596676461"
    ],
    [
      "11980794/25",
      "41308358697/125"
    ],
    [
      "147291081/64",
      "1787514072571/512"
    ],
    [
      "118685436/289",
      "1285001750394/4913"
    ],
    [
      "3179254932/1681",
      "179250606250237/68921"
    ],
    [
      "21490187992/31329",
      "3146192923859317/5545233"
    ],
    [
      "4684002947694/1062961",
      "10137329749327540203/1095912791"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t = -93/13 of a generic rank-4 Mordell family obtained from the Burkhardt quartic, with affine parameters (a,b,c,d) = (-10,-32,-9,-4).\r\n\r\nFound by varying the Burkhardt parameters using the rational parametrization of Bruin–Nasserden, followed by a sixth-power-residue Mestre–Nagao sieve and conductor-aware candidate selection.\r\n\r\nPARI/GP 2.17.4 establishes exact rank 11, with bounds [11,11] and 11 independent rational points.",
  "created_at": "2026-10-23 20:55:23",
  "updated_at": "2026-10-23 20:55:23"
}