{
  "id": 5319,
  "curve_key": "0:116876455200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-135273675"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 50.96876655077368,
  "faltings_height": 2.3050531216894354,
  "conductor": "43828670700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "79"
  ],
  "discriminant": "-7905153807938430000",
  "regulator": "1213.169027749376293729471024560155780107618126",
  "points": [
    [
      "4819",
      "334328"
    ],
    [
      "2449/4",
      "77657/8"
    ],
    [
      "14299/25",
      "899968/125"
    ],
    [
      "413881/400",
      "249477971/8000"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 120870 (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 13:08:53",
  "updated_at": "2026-10-21 13:08:53"
}