{
  "id": 5479,
  "curve_key": "10848:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-226",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 27.87520803054053,
  "faltings_height": 0.3911744141865346,
  "conductor": "3268864",
  "bad_primes": [
    "2",
    "113"
  ],
  "discriminant": "738763264",
  "regulator": "23.613161797424903193439563026951983962731210",
  "points": [
    [
      "-8",
      "36"
    ],
    [
      "-1",
      "15"
    ],
    [
      "-128/9",
      "496/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 - 226x. Found in a bounded exact small-coefficient sweep over every nonzero integer A with -300 <= A <= 300 in y^2 = x^3 + Ax. Each curve was exactly minimalized and compared by c4:c6 identity against the current ICARM database.\r\n\r\nPARI/GP 2.17.4 returned rank bounds [3,3], rational torsion Z/2Z generated by [0,0], conductor 3268864 and minimal discriminant 738763264. Exact quadratic-character certification at 9 good primes gives an F_2 matrix of rank 4 with torsion-row rank 1, proving the three submitted points independent modulo torsion.\r\n\r\nNo novelty claim is made beyond absence from the checked ICARM snapshot and this bounded search.",
  "created_at": "2026-10-22 09:36:07",
  "updated_at": "2026-10-22 09:36:07"
}