{
  "id": 1109,
  "curve_key": "31515195865345993251691556869393:-176915825145895789930299478405474581619598811385",
  "ainvs": [
    "1",
    "0",
    "0",
    "-656566580528041526076907434779",
    "204763686511453405853594537484357296391508689"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4,
    2
  ],
  "naive_height": 217.5840678832653,
  "faltings_height": 15.791985062393907,
  "conductor": "1286799043897115641009631514",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "29",
    "31",
    "41",
    "47",
    "53",
    "61",
    "113",
    "193",
    "281",
    "599",
    "613"
  ],
  "discriminant": "1112228025484236676570331418931289835048770897052666916176534438963354782161972252114944",
  "regulator": "405796.892122181674849267535054488783586908307747047466",
  "points": [
    [
      "50900064512542",
      "13094895084332895785329"
    ],
    [
      "311089955373442",
      "5533421800790073001189"
    ],
    [
      "334153933123486",
      "4762417864510138878577"
    ],
    [
      "365015487014878",
      "3706754651255271985201"
    ],
    [
      "-371832437144672",
      "-19937078913637958859689"
    ],
    [
      "-70309868476526",
      "-15829694250402987332231"
    ],
    [
      "469950833947294",
      "9772969417713770737"
    ],
    [
      "464505611873086",
      "95361784093264808497"
    ]
  ],
  "submitter": "dujella",
  "history": [],
  "commentary": "found by Dujella - Peral (2016)",
  "created_at": "2026-09-23 20:13:35",
  "updated_at": "2026-09-23 20:13:35"
}