{
  "id": 1165,
  "curve_key": "4094980240691432866625296:-8286625546576176673504797136603742656",
  "ainvs": [
    "0",
    "1",
    "0",
    "-85312088347738184721360",
    "9591001789990285638959083957643508"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 170.01541237176752,
  "faltings_height": 11.611917762204328,
  "conductor": "104034096695931795120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "37",
    "41",
    "137",
    "191",
    "557"
  ],
  "discriminant": "230098075517057333158097736420616207787600992133437500000000000",
  "regulator": "11348194.14970519083630702006996408532292227619385686",
  "points": [
    [
      "9002374979964/49",
      "-3735458139436968750/343"
    ],
    [
      "89534682583119/529",
      "-5358807157183593750/12167"
    ],
    [
      "8280909901839/49",
      "88901839021968750/343"
    ],
    [
      "28501737605559/169",
      "-21315249747921150/2197"
    ],
    [
      "21183599969031/121",
      "-6132781609120286250/1331"
    ],
    [
      "20407426032156/121",
      "20214407586843750/1331"
    ],
    [
      "45776144464640676/271441",
      "38900119143759851250/141420761"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1089 and mapping all 7 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 21:38:06",
  "updated_at": "2026-09-23 21:38:06"
}