{
  "id": 5658,
  "curve_key": "0:320247432",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-370657"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 39.169208959947206,
  "faltings_height": 1.3217566557872293,
  "conductor": "120092787",
  "bad_primes": [
    "3",
    "19",
    "37"
  ],
  "discriminant": "-59350936170483",
  "regulator": "22.309009909066142652105397361169441332586947",
  "points": [
    [
      "703",
      "18629"
    ],
    [
      "4921/4",
      "345169/8"
    ],
    [
      "703/9",
      "8774/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Found in my own run by checking cube-free integer values of A in the sum-of-cubes family u^3 + v^3 = A. The specialization A = 6327 gives the global minimal model Y^2 + Y = X^3 - 370657.\r\n\r\nThe explicit map is u = (A + 6Y + 3)/(6X) and v = (A - 6Y - 3)/(6X), with A = 6327. The three submitted points correspond to (u,v) = (28,-25), (503/14,-479/14), and (53/3,28/3).\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 120092787.",
  "created_at": "2026-10-24 00:52:34",
  "updated_at": "2026-10-24 00:52:34"
}