{
  "id": 5805,
  "curve_key": "0:50268195502400294003232",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-58180781831481821763"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 104.54331906764436,
  "faltings_height": 6.769599164761992,
  "conductor": "232723127325927287052",
  "bad_primes": [
    "2",
    "3",
    "19",
    "149",
    "307",
    "563"
  ],
  "discriminant": "-1462321457793713626406046890633073784969008",
  "regulator": "825038.423663842476395175662330830880449757985291",
  "points": [
    [
      "3883243",
      "613902988"
    ],
    [
      "4542679",
      "5963357726"
    ],
    [
      "16458577/4",
      "27107334649/8"
    ],
    [
      "9398184553/1156",
      "860363252089813/39304"
    ],
    [
      "91397918464864393/9096581376",
      "26827333482518662379946587/867595545317376"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(18,-19,-1,1) and specialization t=9/13. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=2935877226. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 10:57:40",
  "updated_at": "2026-10-25 10:57:40"
}