{
  "id": 1134,
  "curve_key": "-3495731156576:-37147196881908037088",
  "ainvs": [
    "0",
    "-1",
    "0",
    "72827732429",
    "42994416559630900"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "naive_height": 90.12283997631233,
  "faltings_height": 5.571946407429548,
  "conductor": "1321186210228868621060280",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "8420798017"
  ],
  "discriminant": "-823282724219542148027966839348392240",
  "regulator": "131996664.7939473882806577724748567563409267747789741",
  "points": [
    [
      "-2939134000/11881",
      "128456738510970/1295029"
    ],
    [
      "7058563149/16129",
      "815971226925059/2048383"
    ],
    [
      "30186301629/19321",
      "5351344815100447/2685619"
    ],
    [
      "49520329349/39601",
      "11391342109618563/7880599"
    ],
    [
      "419139209904/218089",
      "274829393063178526/101847563"
    ],
    [
      "47584515021/93025",
      "13128003940452269/28372625"
    ],
    [
      "4033592343869/1974025",
      "8191545229924947753/2773505125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#26 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 21:37:06",
  "updated_at": "2026-09-23 21:37:06"
}