{
  "id": 5322,
  "curve_key": "0:360359749152",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-417083043"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 53.220737345251024,
  "faltings_height": 2.492717354562547,
  "conductor": "135134905932",
  "bad_primes": [
    "2",
    "3",
    "13",
    "907"
  ],
  "discriminant": "-75149970375516414768",
  "regulator": "594.7376671857399797669783317517039691238051987",
  "points": [
    [
      "907",
      "18140"
    ],
    [
      "11791/9",
      "1155518/27"
    ],
    [
      "30433/16",
      "5145647/64"
    ],
    [
      "2275663/2601",
      "2108490202/132651"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 212238 (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 13:09:09",
  "updated_at": "2026-10-21 13:09:09"
}