{
  "id": 5325,
  "curve_key": "0:493763568768",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-571485612"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 53.85064526766652,
  "faltings_height": 2.545209681430505,
  "conductor": "46290334572",
  "bad_primes": [
    "2",
    "3",
    "67",
    "103"
  ],
  "discriminant": "-141089387640342283008",
  "regulator": "551.3322247734175678025697854399324257517050915",
  "points": [
    [
      "2077",
      "91589"
    ],
    [
      "6901",
      "572783"
    ],
    [
      "21733",
      "3203815"
    ],
    [
      "20569/4",
      "2943779/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 248436 (Weierstrass model y^2 = x^3 - 432k^2, minimal model shown). Found in an exhaustive scan of cube-free k <= 7*10^5 by minimal-model naive height, with a Mestre-Nagao a_p sieve (p = 1 mod 3) and PARI ellrank 2-descent; companion to #5313 (k = 111690).",
  "created_at": "2026-10-21 13:09:23",
  "updated_at": "2026-10-21 13:09:23"
}