{
  "id": 5323,
  "curve_key": "0:432204514848",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-500236707"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 53.584329454330934,
  "faltings_height": 2.5230166969858736,
  "conductor": "162076693068",
  "bad_primes": [
    "2",
    "3",
    "37",
    "349"
  ],
  "discriminant": "-108102281629048062768",
  "regulator": "619.7925933893859668674832839842741446136363122",
  "points": [
    [
      "2443",
      "118660"
    ],
    [
      "5143",
      "368150"
    ],
    [
      "12913/16",
      "322825/64"
    ],
    [
      "26899/25",
      "3412732/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 232434 (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 13:09:14",
  "updated_at": "2026-10-21 13:09:14"
}