{
  "id": 5426,
  "curve_key": "0:127008",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-147"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 23.504010711165584,
  "faltings_height": 0.01632346838876066,
  "conductor": "47628",
  "bad_primes": [
    "2",
    "3",
    "7"
  ],
  "discriminant": "-9335088",
  "regulator": "2.96085078993647567966740305647744820503279",
  "points": [
    [
      "7",
      "14"
    ],
    [
      "49/4",
      "329/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 126. Applying the standard Mordell transformation gives y^2 = x^3 - 432*126^2; rational sixth-power reduction with scale 6 yields the minimal model y^2 = x^3 - 147. PARI/GP 2.17.4 returned exact rank bounds [2,2], with generators [7,14] and [49/4,329/8], trivial rational torsion, conductor 47628, minimal discriminant -9335088, and bad primes 2, 3 and 7. Found in a bounded exact small-model sweep.",
  "created_at": "2026-10-21 23:43:24",
  "updated_at": "2026-10-21 23:43:24"
}