{
  "id": 5531,
  "curve_key": "0:985608",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-1141"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 27.602027977223134,
  "faltings_height": 0.3578249072268899,
  "conductor": "4563",
  "bad_primes": [
    "3",
    "13"
  ],
  "discriminant": "-562166163",
  "regulator": "1.310302718837432720395850740838747487844",
  "points": [
    [
      "13",
      "32"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Cube-sum curve x^3 + y^3 = 13, obtained in my own bounded ascending scan of cube-free integers 1 <= A <= 2000. Its standard Mordell presentation Y^2 = X^3 - 432*13^2 = X^3 - 73008 was reduced by the change [u,r,s,t] = [2,0,0,4] to the global minimal model y^2 + y = x^3 - 1141. The Mordell point [52,260] transports under this change to [13,32] on the minimal model. This point was checked exactly and establishes rank at least 1. The rational torsion subgroup is trivial, the conductor is 4563, and the minimal discriminant is -562166163.",
  "created_at": "2026-10-22 22:27:41",
  "updated_at": "2026-10-22 22:27:41"
}