{
  "id": 6364,
  "curve_key": "297361339755814618681:-5127748930685389125578156766829",
  "ainvs": [
    "1",
    "0",
    "1",
    "-6195027911579471223",
    "5934894595184429532343095878"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 141.42443911611838,
  "faltings_height": 9.253935019606777,
  "conductor": "4355035050839617990",
  "bad_primes": [
    "2",
    "5",
    "17",
    "23",
    "43",
    "47",
    "67",
    "173",
    "229",
    "397",
    "523"
  ],
  "discriminant": "313237898295899946611215636899024960706171667562500",
  "regulator": "27740.659202399797155775266020814263748375481605835",
  "points": [
    [
      "1158849757",
      "17664224773272"
    ],
    [
      "1612073888",
      "11724415590178"
    ],
    [
      "8243661059",
      "717691824233470"
    ],
    [
      "-343173374011/121",
      "35009097486170920/1331"
    ],
    [
      "24705276269/16",
      "455408661573355/64"
    ],
    [
      "7241499509254/5041",
      "10999175151160155/357911"
    ]
  ],
  "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=-1955/137362. Clearing denominators gives the integral model [139317,264720685,36362562732970,0,0], 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 14:25:20",
  "updated_at": "2026-11-01 14:25:20"
}