{
  "id": 5527,
  "curve_key": "0:13625064",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-15770"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 32.854843191500514,
  "faltings_height": 0.7955595084166713,
  "conductor": "107431926507",
  "bad_primes": [
    "3",
    "63079"
  ],
  "discriminant": "-107431926507",
  "regulator": "1299.31690521653805008983488739495178650305568676",
  "points": [
    [
      "26",
      "42"
    ],
    [
      "50",
      "330"
    ],
    [
      "305/4",
      "5227/8"
    ],
    [
      "785/16",
      "20441/64"
    ],
    [
      "232/9",
      "982/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Mordell curve y^2 + y = x^3 - 15770, 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,-15770) 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 107431926507, and the minimal discriminant is -107431926507.",
  "created_at": "2026-10-22 21:50:50",
  "updated_at": "2026-10-22 21:50:50"
}