{
  "id": 5514,
  "curve_key": "235248:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-4901",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 37.105186667452315,
  "faltings_height": 1.16033930059585,
  "conductor": "4548128",
  "bad_primes": [
    "2",
    "13",
    "29"
  ],
  "discriminant": "7534146860864",
  "regulator": "14.416664020901753116598566769370145092021815",
  "points": [
    [
      "-52",
      "338"
    ],
    [
      "117",
      "1014"
    ],
    [
      "-3393/49",
      "29406/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 - 4901x, obtained in my own bounded search in the family y^2 = x^3 + Ax with 0 < |A| <= 30000. Integer seed points were generated using A = (y^2 - x^3)/x for nonzero integer x between -173 and 5000, retaining integral A. This search produced A = -4901. Three independent rational points were recovered and checked exactly on this minimal model, establishing rank at least 3. The rational torsion subgroup is Z/2Z and the conductor is 4548128.",
  "created_at": "2026-10-22 21:13:02",
  "updated_at": "2026-10-22 21:13:02"
}