{
  "id": 5510,
  "curve_key": "73200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1525",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 33.60285209984821,
  "faltings_height": 0.8684780866288412,
  "conductor": "2976800",
  "bad_primes": [
    "2",
    "5",
    "61"
  ],
  "discriminant": "226981000000",
  "regulator": "10.853095915241060114361683048522940188131832",
  "points": [
    [
      "-25",
      "150"
    ],
    [
      "-9",
      "114"
    ],
    [
      "45",
      "150"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 - 1525x, 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. The search model had A = -24400; the rational scaling x = X/4, y = Y/8 gives this minimal model. Three independent rational points were recovered and checked exactly, establishing rank at least 3. The rational torsion subgroup is Z/2Z and the conductor is 2976800.",
  "created_at": "2026-10-22 20:58:08",
  "updated_at": "2026-10-22 20:58:08"
}