{
  "id": 5516,
  "curve_key": "278160:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5795",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 37.60785530004523,
  "faltings_height": 1.2022283533119262,
  "conductor": "2149249600",
  "bad_primes": [
    "2",
    "5",
    "19",
    "61"
  ],
  "discriminant": "12454901432000",
  "regulator": "212.3130761482410589499796930126213636654855956",
  "points": [
    [
      "-76",
      "38"
    ],
    [
      "80",
      "220"
    ],
    [
      "320",
      "5560"
    ],
    [
      "-855/16",
      "25365/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 - 5795x, 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 = -5795. Four independent rational points were recovered and checked exactly on this minimal model, establishing rank at least 4. The rational torsion subgroup is Z/2Z and the conductor is 2149249600.",
  "created_at": "2026-10-22 21:20:59",
  "updated_at": "2026-10-22 21:20:59"
}