{
  "id": 5712,
  "curve_key": "0:-574392738738396888",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "664806410576848"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 81.78417954218529,
  "faltings_height": 4.87300420430707,
  "conductor": "63643329150346501736733922108041",
  "bad_primes": [
    "3",
    "53",
    "514867",
    "97450543"
  ],
  "discriminant": "-190929987451039505210201766324123",
  "regulator": "17694714098328871.4685930978468990786967605394450949808376390",
  "points": [
    [
      "-664453672580042/7625306329",
      "1184729648398231703909/665864624567267"
    ],
    [
      "-367602067989008/13430260321",
      "39506708513774912810783/1556419438340369"
    ],
    [
      "627991749450658/27430978129",
      "118193550875799636795944/4543200890659367"
    ],
    [
      "1097683550721532/32843950441",
      "157722632025331446178043/5952276294471989"
    ],
    [
      "1676630214933994/38956890625",
      "209805095534917915087097/7689116287109375"
    ],
    [
      "44107332706547272/263137194961",
      "9895536151030000609914263/134981223761949209"
    ],
    [
      "5740923125778673897/147937498657936",
      "48390549011662078083320007467/1799357286926534618816"
    ],
    [
      "32047566782568164092/1558389236120721",
      "1596554406946021566544231801328/61519657617976239192519"
    ],
    [
      "5006750861175341663809/133423319850264900",
      "1305579219758542819577280312220627/48735745516318424938893000"
    ],
    [
      "36103134693051312076/705337190494225",
      "529473746118182612800315854199/18732475592525868981625"
    ],
    [
      "-491199449993618726470310577251500183631/28801483171448682936254982426008100",
      "125557749306239311069567570741857725089538250461658744647653/4887899630234335876846185728423614965221222489271000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of the Burkhardt-quartic Mordell curve obtained from parameters (u,v,w)=(-9/4,1/2,-3/2) and t=-617/824. Eleven rational points were reconstructed through the explicit 3-isogeny and transformed onto the minimal model. Their coordinates were verified using exact rational arithmetic, and PARI/GP 2.17.4 returned matching computational rank bounds [11,11].",
  "created_at": "2026-10-24 14:44:12",
  "updated_at": "2026-10-24 14:44:12"
}