{
  "id": 5487,
  "curve_key": "-21360:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "445",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 29.907825879222393,
  "faltings_height": 0.5605592349100232,
  "conductor": "12673600",
  "bad_primes": [
    "2",
    "5",
    "89"
  ],
  "discriminant": "-5639752000",
  "regulator": "60.392731828933264178460683205418491655786186",
  "points": [
    [
      "20",
      "130"
    ],
    [
      "80",
      "740"
    ],
    [
      "49/36",
      "5327/216"
    ]
  ],
  "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 + 445x has rational torsion Z/2Z generated by [0,0].\r\n\r\nPARI/GP 2.17.4 returned rank bounds [3,3], conductor 12673600 and minimal discriminant -5639752000. 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 11:29:20",
  "updated_at": "2026-10-22 11:29:20"
}