{
  "id": 5486,
  "curve_key": "-27792:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "579",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 30.697510465442658,
  "faltings_height": 0.626366283761712,
  "conductor": "10727712",
  "bad_primes": [
    "2",
    "3",
    "193"
  ],
  "discriminant": "-12422690496",
  "regulator": "30.924784200162360768171168534411479720567943",
  "points": [
    [
      "3",
      "42"
    ],
    [
      "48",
      "372"
    ],
    [
      "147",
      "1806"
    ]
  ],
  "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 + 579x has rational torsion Z/2Z generated by [0,0].\r\n\r\nPARI/GP 2.17.4 returned rank bounds [3,3], conductor 10727712 and minimal discriminant -12422690496. 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.",
  "created_at": "2026-10-22 11:03:13",
  "updated_at": "2026-10-22 11:03:13"
}