{
  "id": 6065,
  "curve_key": "279330254041:-147630797058498589",
  "ainvs": [
    "1",
    "0",
    "1",
    "-5819380293",
    "170868493128608"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 79.06698187494015,
  "faltings_height": 3.8312982315501967,
  "conductor": "38475170",
  "bad_primes": [
    "2",
    "5",
    "29",
    "181",
    "733"
  ],
  "discriminant": "146418221314250000",
  "regulator": "151.92399946059313344283585545831347759897049",
  "points": [
    [
      "163851/4",
      "8688395/8"
    ],
    [
      "44827",
      "263410"
    ],
    [
      "5334979/121",
      "-6245130/1331"
    ]
  ],
  "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=1/724. Clearing denominators with x=X/724^2 and y=Y/724^3 gives [723,-725,-524900,0,0]; the displayed equation is its global minimal model, with discriminant 146418221314250000. 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 18:30:19",
  "updated_at": "2026-10-28 18:30:19"
}