{
  "id": 5509,
  "curve_key": "-249120:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "5190",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 37.27706996120347,
  "faltings_height": 1.1746629084084468,
  "conductor": "1723910400",
  "bad_primes": [
    "2",
    "3",
    "5",
    "173"
  ],
  "discriminant": "-8947094976000",
  "regulator": "146.4197101827042792993577306522180852478978702",
  "points": [
    [
      "10",
      "230"
    ],
    [
      "15",
      "285"
    ],
    [
      "24",
      "372"
    ],
    [
      "1176",
      "40404"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + 5190x, obtained in my own bounded search in the family y^2 = x^3 + Ax with 0 < |A| <= 30000. Integer points were generated using A = (y^2 - x^3)/x for nonzero integer x between -173 and 5000, retaining integral A. Four independent rational points were recovered and checked exactly on this model, establishing rank at least 4. The rational torsion subgroup is Z/2Z and the conductor is 1723910400.",
  "created_at": "2026-10-22 20:53:44",
  "updated_at": "2026-10-22 20:53:44"
}