{
  "id": 5320,
  "curve_key": "0:134462608200",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-155628019"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 51.24910398277906,
  "faltings_height": 2.3284145743565507,
  "conductor": "50423478075",
  "bad_primes": [
    "3",
    "5",
    "43",
    "67"
  ],
  "discriminant": "-10463074655061751875",
  "regulator": "298.0609828765890244860175746489709586739612612",
  "points": [
    [
      "2881/4",
      "118117/8"
    ],
    [
      "2881",
      "154133"
    ],
    [
      "8509/9",
      "708947/27"
    ],
    [
      "141169/256",
      "14221449/4096"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 129645 (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 13:08:58",
  "updated_at": "2026-10-21 13:08:58"
}