{
  "id": 1135,
  "curve_key": "13115720912461264228576:1493724922731851300052448533322976",
  "ainvs": [
    "0",
    "1",
    "0",
    "-273244185676276338095",
    "-1728848290289983362878722359600"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "naive_height": 152.78429559968276,
  "faltings_height": 10.57219699136441,
  "conductor": "104034096695931795120",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "29",
    "37",
    "41",
    "137",
    "191",
    "557"
  ],
  "discriminant": "14456116515114485104741059623665082731055450521922541111886800",
  "regulator": "1452568851.162264427047298568955402921334051352813678",
  "points": [
    [
      "-73641212573375/7744",
      "-66831197917789048065/681472"
    ],
    [
      "-231170378234384/24025",
      "362469290922923614536/3723875"
    ],
    [
      "1158549043644400/34969",
      "33075834757354026203160/6539203"
    ],
    [
      "-23299990715956880/2405601",
      "-355340248761564245727080/3731087151"
    ],
    [
      "-248406842384/25",
      "-8993959156789464/125"
    ],
    [
      "2652113546905/64",
      "-3902910872463518685/512"
    ],
    [
      "2010014284101169681/43264",
      "-2849697019098265295032786695/8998912"
    ]
  ],
  "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 21:37:08",
  "updated_at": "2026-09-23 21:37:08"
}