{
  "id": 5838,
  "curve_key": "0:4485962690590752",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-5192086447443"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 72.07945902823926,
  "faltings_height": 4.0642774948115665,
  "conductor": "1682236008971532",
  "bad_primes": [
    "2",
    "3",
    "7",
    "71",
    "2647"
  ],
  "discriminant": "-11645753044775589677334923568",
  "regulator": "35079.3986695157083859852498003155567691059404910",
  "points": [
    [
      "51499",
      "11462584"
    ],
    [
      "129703",
      "46656022"
    ],
    [
      "1191463",
      "1300529398"
    ],
    [
      "79177/4",
      "12808859/8"
    ],
    [
      "6625441/100",
      "16900928239/1000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(5,-3,-1,-2) and specialization t=16/9. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=23680062. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:04:52",
  "updated_at": "2026-10-25 11:04:52"
}