{
  "id": 5526,
  "curve_key": "0:13257864",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-15345"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 32.8002028875468,
  "faltings_height": 0.7910061497538622,
  "conductor": "101719304307",
  "bad_primes": [
    "3",
    "61379"
  ],
  "discriminant": "-101719304307",
  "regulator": "1517.79524708459199865628722737887310357193726587",
  "points": [
    [
      "33",
      "143"
    ],
    [
      "51",
      "342"
    ],
    [
      "345/4",
      "6327/8"
    ],
    [
      "123",
      "1358"
    ],
    [
      "385/9",
      "6760/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Mordell curve y^2 + y = x^3 - 15345, obtained in my own bounded search of the models y^2 + t*y = x^3 + B with t = 0 or 1 and 0 < |B| <= 100000. Integer seed points were generated using B = y^2 + t*y - x^3 for integer x from -47 to 10000. The specialization (t,B) = (1,-15345) supplied six integral seed points. Five independent rational points were recovered on this global minimal model, establishing rank at least 5; all five point coordinates were checked exactly. The rational torsion subgroup is trivial, the conductor is 101719304307, and the minimal discriminant is -101719304307.",
  "created_at": "2026-10-22 21:47:10",
  "updated_at": "2026-10-22 21:47:10"
}