{
  "id": 5723,
  "curve_key": "0:235011515427276431400",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-272004068781569944"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 93.81233237730926,
  "faltings_height": 5.875350273900733,
  "conductor": "1278481768134837687888432658099974675",
  "bad_primes": [
    "3",
    "5",
    "19181",
    "756315294737"
  ],
  "discriminant": "-31962044203370942197210816452499366875",
  "regulator": "78941393174497501.626398144799322853750915674246077390589655795",
  "points": [
    [
      "23098001843145164281/1944870111396",
      "111000862908343899236863987201/2712288629171302056"
    ],
    [
      "1879999901150747815801/7348404110436",
      "81514850450374865160375587341559/19920009772145246184"
    ],
    [
      "362869680877515934/7056504009",
      "-218587634270925858555453728/592767506268027"
    ],
    [
      "29721751031970156934/4429791555849",
      "-161963051446014716263123021211/9323413296136281243"
    ],
    [
      "383835796629307576/159150729969",
      "-235486762395189775594089265/63491114761642953"
    ],
    [
      "40057085211273430009/54677240092836",
      "-140754287966828932832464547585/404305712205907075416"
    ],
    [
      "1334615051449197304/2040992248689",
      "254201474199445566147162127/2915828879221312137"
    ],
    [
      "7054638608161228066/7386692315409",
      "15539167842088924558078160912/20075899549357404423"
    ],
    [
      "82910648523373590184/39435297741009",
      "743815182871199270562516663272/247643929294994490777"
    ],
    [
      "5493189636179807158096/1618043786757225",
      "405716003838720271115909185142269/65085673788587501260875"
    ],
    [
      "16089769082832175868464/24702091103282121",
      "255732460267120032153736233853640/3882402684888745539345669"
    ],
    [
      "1753197306090620953337134/67290766734720321",
      "-2321361900580334578411512565867951999/17455537052853333634969119"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of the Mordell curve obtained from the Bruin–Nasserden parametrization of the Burkhardt quartic using (u,v,w)=(3/5,16/5,-14/5) and t=1102/751.  PARI/GP 2.17.4 returned matching computational rank bounds [12,12].",
  "created_at": "2026-10-24 16:54:40",
  "updated_at": "2026-10-24 16:54:40"
}