{
  "id": 1163,
  "curve_key": "-18886226765655624224:62548945085053152130745017376",
  "ainvs": [
    "0",
    "1",
    "0",
    "393463057617825505",
    "-72394612235805314278716750"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 133.15489376321574,
  "faltings_height": 9.200474336558882,
  "conductor": "892331075985258840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "29",
    "53",
    "71",
    "73",
    "313",
    "1319"
  ],
  "discriminant": "-6162552357420272961294560401623129531548558729875575600",
  "regulator": "573339.52012222038967873733037658666980912652469748",
  "points": [
    [
      "11377784475",
      "1215443878690125"
    ],
    [
      "20517117475",
      "2940191186843925"
    ],
    [
      "56107034034850/841",
      "420286179870146333100/24389"
    ],
    [
      "49522392313/16",
      "11231373061214229/64"
    ],
    [
      "400907179",
      "12238626827805"
    ],
    [
      "1090958583695602/196249",
      "36255117897811644511992/86938307"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1111 and mapping all 6 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 21:38:01",
  "updated_at": "2026-09-23 21:38:01"
}