{
  "id": 5825,
  "curve_key": "0:46898209928786416200",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-54280335565725019"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 90.58902236157387,
  "faltings_height": 5.606741105922784,
  "conductor": "72373780754300025",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "41"
  ],
  "discriminant": "-1272825286183171753044779234745151875",
  "regulator": "28700.2637895375604292009041117389572487791251765",
  "points": [
    [
      "378651",
      "3057736"
    ],
    [
      "658749",
      "481231705"
    ],
    [
      "1246609",
      "1372221714"
    ],
    [
      "11707059/25",
      "27502425752/125"
    ],
    [
      "49433839/121",
      "156973774884/1331"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(10,-4,-1,-6) and specialization t=-16/1. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=89674585. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:01:56",
  "updated_at": "2026-10-25 11:01:56"
}