{
  "id": 5611,
  "curve_key": "0:-5986539289512520416",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "6928864918417269"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 86.47209034212985,
  "faltings_height": 5.263663437635783,
  "conductor": "2370823163341903594820345551524",
  "bad_primes": [
    "2",
    "3",
    "1753",
    "146391686599"
  ],
  "discriminant": "-20739961032914972647488382884731952",
  "regulator": "96024000335409228.5274389061821793801974653787850606656842749",
  "points": [
    [
      "3564931117239555/27624766849",
      "437463973407587761365084/4591429623671743"
    ],
    [
      "1378210292013394903/1239060623161",
      "1622048406881648910186677554/1379236790519827091"
    ],
    [
      "188847890751468342588318271/207358302333122161",
      "2595184315602210062765333916887187285490/94423945375862483607463159"
    ],
    [
      "-2358417425505913961/22002807211225",
      "7790312509200471394998245962/103208897827801275875"
    ],
    [
      "28634076621379610025/164075297219344",
      "232556072740277568789463319061/2101671328238454532672"
    ],
    [
      "-4645140270603876642207/24374795176998436",
      "10621102813469303078570615450289/3805497688403485859604184"
    ],
    [
      "8757013835377001891305/33495773538472036",
      "965364620495914945629144907805717/6130346430325485551498216"
    ],
    [
      "-342937811109384361178694183/2025549151705520017984",
      "4153411855020753616473808831355685216867/91162070253072325450811165275648"
    ],
    [
      "-28900647762157044392998967/627643320763274724496",
      "1299627739623803799625811006417916429061/15724229262032528656043358539456"
    ],
    [
      "84065101488360268639475833/354729900310901947456",
      "950455540718024988943276664940192116429/6681080356961831057035506576896"
    ],
    [
      "3051645137651656799074080127/18934995061929944529",
      "168578057572086818128678706263503872403782/82394418736799303677104919833"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact-rank-11 Mordell curve obtained by the rational 3-isogeny from y^2=x^3-256624626608047, discovered using the Burkhardt quartic construction with parameters (u,v,w)=(11,-8,2) and t=-645/722.\r\n\r\n",
  "created_at": "2026-10-23 22:41:58",
  "updated_at": "2026-10-23 22:41:58"
}