{
  "id": 6362,
  "curve_key": "8180501079842046081:-23350391770647097827602659521",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-170427105830042627",
    "27025916443818695239458179"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 130.6448552380073,
  "faltings_height": 8.686738004940786,
  "conductor": "12853086609924990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "67",
    "79",
    "277",
    "751",
    "907"
  ],
  "discriminant": "1275016020496999202067013320019872870113395776000000",
  "regulator": "10304.861285884743592669315436894203960611466932029",
  "points": [
    [
      "-476149563",
      "472295415406"
    ],
    [
      "163928187",
      "1868945065906"
    ],
    [
      "211195467",
      "672610209106"
    ],
    [
      "228746187",
      "102200839906"
    ],
    [
      "250196187",
      "217861813906"
    ],
    [
      "-1331743422717/2809",
      "167294468909107562/148877"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/6-torsion Kubert–Tate family curve from my rational-parameter search of y^2+(1-c)xy-by=x^3-bx^2, with b=c(c+1), following the construction of David Renshaw on curve#1192 and the c=1/6916 example of Lewis Combes on curve#5970.\r\n\r\nHere c=-5540/74349. Clearing denominators gives the integral model [79889,381201860,28341977089140,0,0], which reduces to the displayed global minimal model.\r\n\r\nThe completed rank-6 batch identified this specialization. A separate rank computation on the minimal model returned bounds [6,6] and the six displayed rational points. All six points were checked exactly on this model. The minimal discriminant was fully factored and every listed bad-reduction prime proved prime.",
  "created_at": "2026-11-01 14:20:21",
  "updated_at": "2026-11-01 14:20:21"
}