{
  "id": 1144,
  "curve_key": "109173327100521832801:963256216829216270473380949199",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2274444314594204850",
    "-1114879880778907709634448725"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "naive_height": 138.41840535014015,
  "faltings_height": 9.530925001945306,
  "conductor": "965575150587952905",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "137",
    "173",
    "347",
    "617"
  ],
  "discriminant": "216061451167651643918817073979733942195905858470134471225",
  "regulator": "276991.02745939693646544486082098299243157800924115",
  "points": [
    [
      "-11059644963/16",
      "-721259523603501/64"
    ],
    [
      "-2304249597/4",
      "-16347624543909/8"
    ],
    [
      "-27544064766/25",
      "-915160944861333/125"
    ],
    [
      "-806505198",
      "-13959520242129"
    ],
    [
      "-643604670",
      "-9075177562365"
    ],
    [
      "705575639106",
      "-592672303525047453"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Obtained by computing a rational isogeny from curve#1112 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 21:37:30",
  "updated_at": "2026-09-23 21:37:30"
}