{
  "id": 3614,
  "curve_key": "171132819233279301219219161204961:-2247315059599383659461052394966095227488097984209",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3565267067359985442067065858437",
    "2601059096758546793470762667503415178211022461"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 222.66764132105652,
  "faltings_height": 16.380489355593024,
  "conductor": "4676874174796470773416020830070114756053796903425726941833510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "29",
    "31",
    "67",
    "73",
    "2657",
    "6869",
    "12823",
    "53731",
    "590041",
    "2195876051",
    "495817494960962003"
  ],
  "discriminant": "-22311124624690959275070379946838892108196808696456112997145794406036039598955529515520000000",
  "regulator": "2398678809590617282348.939480971291982573348394892842241946097055059402571858",
  "points": [
    [
      "-4035468161546801/4",
      "575282993300551131437047/8"
    ],
    [
      "1054975905594751",
      "3734857902826730923904"
    ],
    [
      "1421894538852991",
      "20159093159524809503744"
    ],
    [
      "1517098651692379",
      "26152126715118708732704"
    ],
    [
      "49438990988456671",
      "10984798715620381964013824"
    ],
    [
      "-6799943126875076561/18769",
      "159448526204414460536231469952/2571353"
    ],
    [
      "-78306058195767689/81",
      "52286351306067454884040736/729"
    ],
    [
      "7700715620100055/9",
      "359122041911391998068064/27"
    ],
    [
      "11152281158257711/81",
      "33508588206793388230094336/729"
    ],
    [
      "52782719537125519/49",
      "1111085285404896192490112/343"
    ],
    [
      "117908245458862439/169",
      "46772906677458739631576048/2197"
    ],
    [
      "185854137748312439/169",
      "7033144099287252551810048/2197"
    ],
    [
      "381079020296745569/49",
      "228876946242866716277266412/343"
    ],
    [
      "575819901757041431/361",
      "213892886492118012344511616/6859"
    ],
    [
      "36762809583368746759/6889",
      "210511650962795611718236460608/571787"
    ],
    [
      "153517881489488677999/120409",
      "472664743874217314242686701152/41781923"
    ],
    [
      "708573019102153441639/582169",
      "3573631971364685200974967547648/444194947"
    ],
    [
      "9404609085806083568839/635209",
      "904955252883921174311806691994352/506261573"
    ],
    [
      "86282090478964775537639/60637369",
      "9548798453897790651965939030820352/472183192403"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -1/11 of the rank-17 fibration of X1092, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #3432 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:19:35",
  "updated_at": "2026-09-29 19:19:35"
}