{
  "id": 6366,
  "curve_key": "358458489554808256:-4161549846011568605432896096",
  "ainvs": [
    "0",
    "1",
    "0",
    "-7467885199058505",
    "4816608615579650078824128"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 127.19137014973376,
  "faltings_height": 8.657103302783444,
  "conductor": "1023993662229363540",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "41",
    "233",
    "911",
    "42457"
  ],
  "discriminant": "-9995623783222345564516598373117516286221614892750000",
  "regulator": "101310.58423980365604939584651121194583786251892177",
  "points": [
    [
      "-155469249",
      "1489911583875"
    ],
    [
      "790764229/9",
      "59392311640145/27"
    ],
    [
      "7432935549/49",
      "918723303337125/343"
    ],
    [
      "15484103037/4",
      "1926366304450731/8"
    ],
    [
      "292830375331/441",
      "158423174413122905/9261"
    ],
    [
      "339013035231/1681",
      "233854864932213525/68921"
    ]
  ],
  "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=11883/42457. Clearing denominators gives the integral model [30574,-645722220,-27415428294540,0,0], 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 14:31:40",
  "updated_at": "2026-11-01 14:31:40"
}