{
  "id": 6062,
  "curve_key": "524449666729:-379800664855830037",
  "ainvs": [
    "1",
    "0",
    "1",
    "-10926034724",
    "439583192339502"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 80.95684588765857,
  "faltings_height": 3.977167907355594,
  "conductor": "47350030",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "61",
    "853"
  ],
  "discriminant": "382489523174753540",
  "regulator": "252.88408783124231417460330798696549038682239",
  "points": [
    [
      "-105985",
      "20229001"
    ],
    [
      "206427/4",
      "28824571/8"
    ],
    [
      "104356986071/1729225",
      "-68611131714701/2273930875"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own rational-parameter search of the Kubert-Tate family for torsion 6, following the construction described by David Renshaw on curve #1192 and the t=1/6916 example submitted by Lewis Combes on curve #5970. In y^2+(1-c)*x*y-b*y=x^3-b*x^2, set c=t and b=t*(t+1), then specialize at t=-1/854. Clearing denominators with x=X/854^2 and y=Y/854^3 gives [855,853,728462,0,0]; the displayed equation is its global minimal model, with discriminant 382489523174753540. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/6Z.",
  "created_at": "2026-10-28 18:07:32",
  "updated_at": "2026-10-28 18:07:32"
}