{
  "id": 5620,
  "curve_key": "0:96049800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-111169"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 36.760754729855684,
  "faltings_height": 1.1210521366129358,
  "conductor": "36018675",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11"
  ],
  "discriminant": "-5338868101875",
  "regulator": "48.697253424205424627836261042853264088383228",
  "points": [
    [
      "49",
      "80"
    ],
    [
      "91",
      "801"
    ],
    [
      "511",
      "11546"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Found in my own run by checking Mordell curves with coefficients supported on small primes. The coefficient B = -3*1540^2 = -7114800 gives y^2 = x^3 - 7114800. The change x = 4X, y = 8Y + 4 gives the global minimal model Y^2 + Y = X^3 - 111169.\r\n\r\nThis is also the sum-of-cubes curve u^3 + v^3 = 3465, with u = (Y + 578)/X and v = (577 - Y)/X. The three submitted points correspond to (u,v) = (94/7,71/7), (197/13,-32/13), and (1732/73,-1567/73).\r\n\r\nAll three points were checked exactly and are independent. Matching rank bounds [3,3] establish rank exactly 3, with trivial rational torsion and conductor 36018675.",
  "created_at": "2026-10-23 23:43:13",
  "updated_at": "2026-10-23 23:43:13"
}