{
  "id": 5726,
  "curve_key": "0:-16310758341230208",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "18878192524572"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 74.66120261187949,
  "faltings_height": 4.279422793448253,
  "conductor": "9622426130859765856242145968",
  "bad_primes": [
    "2",
    "3",
    "89",
    "457",
    "863",
    "44819"
  ],
  "discriminant": "-153958818093756253699874335488",
  "regulator": "20481589501008.81725186433054199118071077980398257235186850",
  "points": [
    [
      "-4701197906774/178623225",
      "1920458221910770474/2387299402125"
    ],
    [
      "-11393585412971/1195430625",
      "175417329581274933917/41332013859375"
    ],
    [
      "-9355198422782/35733475089",
      "29348971009120685624950/6754805996498937"
    ],
    [
      "1225334502226/502880625",
      "49016680942590231974/11277098015625"
    ],
    [
      "2167334127226/544055625",
      "55229502000467018026/12690097453125"
    ],
    [
      "4775165262291058/172020051009",
      "452745611729022242996810/71345832216135777"
    ],
    [
      "76387317093082/2486917161",
      "857954987358466776490/124020071901909"
    ],
    [
      "17958098736106306/396125478225",
      "2639090923587344805745546/249315434112641625"
    ],
    [
      "9786390274170226/59978459025",
      "970231677574383529807526/14689024507517625"
    ],
    [
      "-708545521976207/77697102564",
      "92190048837032322822025/21657445762894488"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of a Mordell curve constructed using the Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(9/5,-8/5,18/5) and specialization t=80/43. \r\n\r\nThe specialization was selected using a three-stage Mestre–Nagao sieve. \r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [10,10].",
  "created_at": "2026-10-24 16:57:58",
  "updated_at": "2026-10-24 16:57:58"
}