{
  "id": 3491,
  "curve_key": "45511302460502224:-9709098268906553161886272",
  "ainvs": [
    "0",
    "1",
    "0",
    "-948152134593796",
    "11237381939628169443140"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 115.07021128723596,
  "faltings_height": 6.787983175425944,
  "conductor": "8562359590620",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "23",
    "53",
    "727",
    "14639"
  ],
  "discriminant": "17278187955776727061097576436480",
  "regulator": "13789.4368318126082621190765393275902576800533130",
  "points": [
    [
      "71186885/4",
      "1104781425/8"
    ],
    [
      "436885724/25",
      "275255902482/125"
    ],
    [
      "5137773896/289",
      "1810873578/4913"
    ],
    [
      "1049840135971/59049",
      "138331479685058/14348907"
    ],
    [
      "63975424543844/3598609",
      "278891480602482/6826561273"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Rank-5 Z/6Z curve obtained via the 2-isogeny involution\r\nw_2(t) = -(2t+12)/(t+2)\r\nfrom the specialization t = -7336/3657, giving the isogenous parameter t = 14606/11. Found during a conductor/discriminant-first search of the universal X_1(6) family. PARI/GP 2.17.4 gives rank bounds [5,5] and torsion Z/6Z.",
  "created_at": "2026-09-27 10:33:31",
  "updated_at": "2026-09-27 10:33:31"
}