{
  "id": 5734,
  "curve_key": "0:2233855153984165632",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2585480502296488"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 84.50052107073434,
  "faltings_height": 5.099365998352823,
  "conductor": "180487154549393097036530142621888",
  "bad_primes": [
    "2",
    "3",
    "733",
    "440907316217"
  ],
  "discriminant": "-2887794472790289552584482281950208",
  "regulator": "21666945699510707.2905259985173071808689602052261187976635126",
  "points": [
    [
      "212530266880521553/1480244522409",
      "34843347512815166957344195/1800943938922477077"
    ],
    [
      "59893448435640718/261659871729",
      "12982025360933556977217140/133846089205920183"
    ],
    [
      "769567516296746/2675475625",
      "20155602706021088346544/138388976703125"
    ],
    [
      "71297348564494618/73942117929",
      "-19010034694881004540036040/20106562533607467"
    ],
    [
      "128629239372098926/857522300625",
      "-22313563056218252794443076/794087088436265625"
    ],
    [
      "103911191177718935246/28962318172225",
      "1059208185194010021002192469956/155865494026327254625"
    ],
    [
      "881694641798478137297/1045106308234816",
      "26124035196746059877209820037095/33786305423671188068864"
    ],
    [
      "74039395067822458721/385389313882225",
      "-507817717433423376035879609269/7565706726242109520375"
    ],
    [
      "158727655609392112181209/420117167207091600",
      "61703691197272645049100429292995427/272305016819514235084536000"
    ],
    [
      "19227448884236373969242234/9231878783376483025",
      "-84298596697215265129433367274769519648/28050146911566860469815702375"
    ],
    [
      "7386431016920068742826014/8396034327678765625",
      "20036684283983311060508699465000779412/24328274553077333125955078125"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed through the Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(-18/5,1/5,-10/5) and specialization t=-1831/1135. PARI/GP 2.17.4 returned rank bounds [11,11].",
  "created_at": "2026-10-24 17:24:55",
  "updated_at": "2026-10-24 17:24:55"
}