{
  "id": 5845,
  "curve_key": "0:51658146734695200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-59789521683675"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 76.96684861530977,
  "faltings_height": 4.471559960400776,
  "conductor": "79719362244900",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "41",
    "61"
  ],
  "discriminant": "-1544307942166261778920970430000",
  "regulator": "14610.0374615499875128624393523958649436059135304",
  "points": [
    [
      "39711",
      "1683234"
    ],
    [
      "67039",
      "15540238"
    ],
    [
      "92659",
      "27124748"
    ],
    [
      "1407819/25",
      "1362358872/125"
    ],
    [
      "1412089/16",
      "1603371763/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(14,-18,-1,4) and specialization t=7/26. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=2976190. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:06:27",
  "updated_at": "2026-10-25 11:06:27"
}