{
  "id": 5318,
  "curve_key": "0:106916128200",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-123745519"
  ],
  "rank_lower_bound": 4,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 50.79062103088049,
  "faltings_height": 2.290207661698336,
  "conductor": "40093548075",
  "bad_primes": [
    "3",
    "5",
    "7",
    "367"
  ],
  "discriminant": "-6615195873425251875",
  "regulator": "375.2262883638559062809132336544274795569790777",
  "points": [
    [
      "2569/4",
      "95049/8"
    ],
    [
      "2569",
      "129734"
    ],
    [
      "2821",
      "149418"
    ],
    [
      "2391739/25",
      "3698883388/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 115605 (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 13:08:48",
  "updated_at": "2026-10-21 13:08:48"
}