{
  "id": 5525,
  "curve_key": "0:11012328",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-12746"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 32.42905186097878,
  "faltings_height": 0.7600768975398604,
  "conductor": "70180189803",
  "bad_primes": [
    "3",
    "17",
    "2999"
  ],
  "discriminant": "-70180189803",
  "regulator": "1112.67192654514494091511464864359093397524712997",
  "points": [
    [
      "26",
      "69"
    ],
    [
      "32",
      "141"
    ],
    [
      "137/4",
      "1321/8"
    ],
    [
      "206",
      "2954"
    ],
    [
      "268/9",
      "3142/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Mordell curve y^2 + y = x^3 - 12746, 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,-12746) supplied seven 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 70180189803, and the minimal discriminant is -70180189803.",
  "created_at": "2026-10-22 21:39:11",
  "updated_at": "2026-10-22 21:39:11"
}