{
  "id": 6368,
  "curve_key": "22833080882095698256:-108137758935403636889884492096",
  "ainvs": [
    "0",
    "1",
    "0",
    "-475689185043660380",
    "125159443053709666200590628"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 133.72422622251958,
  "faltings_height": 9.003676893063417,
  "conductor": "1023993662229363540",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "41",
    "233",
    "911",
    "42457"
  ],
  "discriminant": "121667985565916617393066429361008374052831141689696000",
  "regulator": "45026.926328801624910842598449427531483494452854120",
  "points": [
    [
      "-739038989",
      "8547806589270"
    ],
    [
      "-6345092",
      "11321549330442"
    ],
    [
      "25641148",
      "10629161985078"
    ],
    [
      "219932371",
      "5583742120110"
    ],
    [
      "537420074256",
      "393976637651192310"
    ],
    [
      "-1091296786361/1849",
      "1125292429260571440/79507"
    ]
  ],
  "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=11872/65227. An integral model is [53355,-915319328,-59703533807456,0,0], 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 14:38:00",
  "updated_at": "2026-11-01 14:38:00"
}