{
  "id": 6058,
  "curve_key": "303107540176:-166876472223567424",
  "ainvs": [
    "0",
    "1",
    "0",
    "-6314740420",
    "193141960160100"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 79.3120604926796,
  "faltings_height": 3.850176452847337,
  "conductor": "102262820",
  "bad_primes": [
    "2",
    "5",
    "11",
    "17",
    "37",
    "739"
  ],
  "discriminant": "165533399405792000",
  "regulator": "308.05765625597931166865828477369370294573992",
  "points": [
    [
      "-13980",
      "16694010"
    ],
    [
      "27404",
      "6377570"
    ],
    [
      "316060720/6889",
      "8310110/571787"
    ]
  ],
  "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=1/739. Clearing denominators with x=X/739^2 and y=Y/739^3 gives [738,-740,-546860,0,0]; the displayed equation is its global minimal model, with discriminant 165533399405792000. 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 17:49:49",
  "updated_at": "2026-10-28 17:49:49"
}