{
  "id": 5425,
  "curve_key": "0:64800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-75"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 22.158121764680732,
  "faltings_height": -0.09583394381831031,
  "conductor": "24300",
  "bad_primes": [
    "2",
    "3",
    "5"
  ],
  "discriminant": "-2430000",
  "regulator": "4.760180787250856601298477196538613680885",
  "points": [
    [
      "91/9",
      "836/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 90. Applying the standard Mordell transformation gives y^2 = x^3 - 432*90^2; rational sixth-power reduction with scale 6 yields the minimal model y^2 = x^3 - 75. PARI/GP 2.17.4 returned exact rank bounds [1,1], with generator [91/9,836/27], trivial rational torsion, conductor 24300, minimal discriminant -2430000, and bad primes 2, 3 and 5. Found in a bounded exact small-model sweep.",
  "created_at": "2026-10-21 23:42:17",
  "updated_at": "2026-10-21 23:42:17"
}