{
  "id": 6436,
  "curve_key": "388187525023872868630803907580281:-7838325734286046288166928652771284603476803487821",
  "ainvs": [
    "1",
    "0",
    "1",
    "-8087240104664018096475081407923",
    "9072136266534775122552825366854145436656183006"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 225.1662194419406,
  "faltings_height": 16.668503500775902,
  "conductor": "9034171088450771262709353690866719130",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "19",
    "31",
    "43",
    "61",
    "103",
    "409",
    "877",
    "997",
    "2969",
    "6037",
    "20323",
    "29789"
  ],
  "discriminant": "-1703440437381973062997347812685748155367049187108159687921589810558345114160102263844031250000",
  "regulator": "54314613261753.6863147490305725636347249139828834732469124128",
  "points": [
    [
      "316347638603050382305/322624",
      "-8367528439075314200358819514211/183250432"
    ],
    [
      "57684670660830587167845022930/118706189286169",
      "93772685817462380854754830598649107555561481/1293332065639672077053"
    ],
    [
      "-1153631728725209460478601045/355219576009",
      "6966442212301212119505795709954767106104/211711932960092027"
    ],
    [
      "121888398234619246406768014849936055/8337372567088069129",
      "-41804383163739030622701686403624270030294540311757084/24073753730714186542767676133"
    ],
    [
      "74257072441044209310374931255/29546595319684",
      "-10918007381480652423257209586248421196489321/160605778154109285752"
    ],
    [
      "4784357699769557744437159439680/917732070692649",
      "9161807368305047626790240098110125357182630889/27801860698645683222357"
    ],
    [
      "15678066786437943938107595547766995/7265087743127094241",
      "800144347983392466444741077128450885008098765418072/19582191606119269167775297711"
    ],
    [
      "4275666580769515103764148270/1467899441761",
      "179867693991828080379124984887309859328868/1778461458754933009"
    ],
    [
      "3394200999060027",
      "143964060783220585041644"
    ],
    [
      "303772997486965885070875895757195/99239459656748401",
      "-3564224887855155272375944467950552170140667635148/31262707436714328347551351"
    ],
    [
      "78916161055703051320492481273395/45941343669383761",
      "-155318534924268721184995491803941062250788734632/9847036316040676482398759"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = 1897/605 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645",
  "created_at": "2026-11-03 04:32:33",
  "updated_at": "2026-11-03 04:32:33"
}