{
  "id": 5485,
  "curve_key": "15456:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-322",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 28.9372576693569,
  "faltings_height": 0.4796785507545652,
  "conductor": "6635776",
  "bad_primes": [
    "2",
    "7",
    "23"
  ],
  "discriminant": "2136719872",
  "regulator": "13.629127935652917022095882932623754853344769",
  "points": [
    [
      "-14",
      "42"
    ],
    [
      "18",
      "6"
    ],
    [
      "-63/4",
      "273/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Found in an exact bounded sweep of quartic twists y^2 = x^3 + Ax over every integer A with 301 <= |A| <= 1500. The model y^2 = x^3 - 322x has rational torsion Z/2Z generated by [0,0].\r\n\r\nPARI/GP 2.17.4 returned rank bounds [3,3], conductor 6635776 and minimal discriminant 2136719872. Exact quadratic-character certification at 10 good primes gives an F_2 matrix of rank 4 with torsion-row rank 1, proving the three submitted points independent modulo torsion.",
  "created_at": "2026-10-22 10:19:07",
  "updated_at": "2026-10-22 10:19:07"
}