{
  "id": 5745,
  "curve_key": "0:-84156857818415932032",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "97403770623166588"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 91.75842817275486,
  "faltings_height": 5.704191590187866,
  "conductor": "35563286457515224348725967345296",
  "bad_primes": [
    "2",
    "3",
    "7",
    "1861",
    "38148308389"
  ],
  "discriminant": "-4098597637655714575741970284610673408",
  "regulator": "97991077624407290.5075551282190292743916509957336792922151840",
  "points": [
    [
      "-1932418664437723/4558005169",
      "44804865009416676171525/307724602974697"
    ],
    [
      "-35790900957905702/105944391081",
      "8365358882639383595646830/34483945797345771"
    ],
    [
      "93586051822834109/119373705025",
      "31390307539685513685760977/41244211954662625"
    ],
    [
      "191904558821452757/190858018129",
      "88002969830411413558926285/83380714954070617"
    ],
    [
      "-25621481423068327958/79079348519649",
      "177057122358608871655755283210/703225522168696317393"
    ],
    [
      "-1984841713426939888486/6884899580337025",
      "154818988550823527481302450113338/571276573723840848797375"
    ],
    [
      "11514965055216223889609986/9612400324865765625",
      "40166293238107476255391931870402079766/29802162207559637097017578125"
    ],
    [
      "1818473317109196375304745098/8283720430150625408481",
      "247750977920305863915937785987290877213590/753942369211446545577895610045871"
    ],
    [
      "4207117521377477446924873738/38823763945993574761161",
      "2402994855905119545869819907513897942882050/7649736160940116778631420164350341"
    ],
    [
      "440211583891544154014664917919698/108685163885786325719588281",
      "9242943138016935655366067654921110311958588866150/1133066493192539092365560282238373423571"
    ],
    [
      "12629249026976452437711652417783751066/62223326691793588384014330625",
      "44881389385442869387657637983386963878169172872806572614/15521362416458035097888900946091007734890625"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of the Burkhardt-quartic Mordell curve constructed using parameters (u,v,w)=(9/6,-9/6,-1/6) and specialization t=-1133/838. \r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [11,11] for this model and its original 3-isogenous curve.",
  "created_at": "2026-10-24 18:14:07",
  "updated_at": "2026-10-24 18:14:07"
}