{
  "id": 5742,
  "curve_key": "0:-1840732336370569176",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "2130477241169640"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 84.11339035045246,
  "faltings_height": 5.067105104996001,
  "conductor": "653606391620419410901518477276489",
  "bad_primes": [
    "3",
    "8521908964678561"
  ],
  "discriminant": "-1960819174861258232704555431829467",
  "regulator": "545730934020.995325053588803135471869483480415478392624536084",
  "points": [
    [
      "-302263/4",
      "329749769/8"
    ],
    [
      "1185849/4",
      "1343106951/8"
    ],
    [
      "319100",
      "186071959"
    ],
    [
      "3700785/4",
      "7128926797/8"
    ],
    [
      "7983425/4",
      "22560153797/8"
    ],
    [
      "-63119506/3025",
      "7662995559097/166375"
    ],
    [
      "-33578335/484",
      "451324244557/10648"
    ],
    [
      "-790688/9",
      "1028975032/27"
    ],
    [
      "1254726641/12100",
      "75826349677811/1331000"
    ],
    [
      "9723474882/9409",
      "959734302315503/912673"
    ],
    [
      "10135616694/3025",
      "1020440214751872/166375"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed using the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(-9/6,-3/6,-1/6) and specialization t=-233/690. The specialization was identified through a three-stage Mestre–Nagao sieve over 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [11,11] for this model and its rationally 3-isogenous partner.",
  "created_at": "2026-10-24 18:11:55",
  "updated_at": "2026-10-24 18:11:55"
}