{
  "id": 1145,
  "curve_key": "1363165027034165270416:50315970305562276445992967004864",
  "ainvs": [
    "0",
    "1",
    "0",
    "-28399271396545109800",
    "-58236076752015354870599489152"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "naive_height": 145.99228852376265,
  "faltings_height": 9.893621517118827,
  "conductor": "892331075985258840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "29",
    "53",
    "71",
    "73",
    "313",
    "1319"
  ],
  "discriminant": "788273668101383807494994476803260459372334827613258777600",
  "regulator": "573339.52012222038967873733037658666980912652469748",
  "points": [
    [
      "-3102201584",
      "-3109857582720"
    ],
    [
      "-3108901384",
      "-2468383847280"
    ],
    [
      "-3115030309",
      "-1444383161970"
    ],
    [
      "-3070442437",
      "-3911106857658"
    ],
    [
      "-573587682492712/187489",
      "291147725115812117280/81182737"
    ],
    [
      "361022171513/16",
      "210217284133151403/64"
    ]
  ],
  "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 21:37:31",
  "updated_at": "2026-09-23 21:37:31"
}