{
  "id": 1166,
  "curve_key": "1136525493768038709024642436576:-1211626524327670334840158055867888679315507424",
  "ainvs": [
    "0",
    "1",
    "0",
    "-23677614453500806438013384095",
    "1402345514268129069082402138467169596598250"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "naive_height": 207.6165857571129,
  "faltings_height": 14.737531237487667,
  "conductor": "1128310354841987032068083640",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "31",
    "41",
    "53",
    "61",
    "67",
    "109",
    "257",
    "263",
    "6857"
  ],
  "discriminant": "3243939912551856986766443772872670662598800835538825751615730275341948376168400",
  "regulator": "233557909.634031665003976922249867242089139925297950721",
  "points": [
    [
      "107419960239779",
      "-313721489863986000615"
    ],
    [
      "216240168419152730/2209",
      "-15598599911447018011100100/103823"
    ],
    [
      "32121862670251235/361",
      "-15707124583829321430645/6859"
    ],
    [
      "114004798064435",
      "-429784753869729330345"
    ],
    [
      "2041095956766964662515/22972849",
      "-13648826374909369892756206335/110108865257"
    ],
    [
      "88849144792595",
      "-140771353409894025"
    ],
    [
      "19107690969364505555/214369",
      "-477627079987455322687410375/99252847"
    ],
    [
      "40709650599438560679467/458088409",
      "4547796063044293821810079028907/9804466217827"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1108 and mapping all 8 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.",
  "created_at": "2026-09-23 21:38:07",
  "updated_at": "2026-09-23 21:38:07"
}