{
  "id": 3524,
  "curve_key": "1493384335004575238199307612891921:-673501661790123521456826701982150382351082832210425",
  "ainvs": [
    "1",
    "1",
    "1",
    "-31112173645928650795818908601915",
    "779515812257087396130143737786847333166985805001"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 234.07314985391193,
  "faltings_height": 17.56392602497794,
  "conductor": "1789399932124511774089607156478992325365460369832460586",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "43",
    "53",
    "71",
    "101",
    "107",
    "113",
    "193",
    "283",
    "491",
    "509",
    "1361",
    "2287",
    "4057",
    "6899",
    "23857",
    "49157",
    "611071"
  ],
  "discriminant": "-260575201105740751487391860696010282171113275960124319765544701277019673067197498463302599673420288",
  "regulator": "3465258965864872.003547908546988461646219807766022946825934367065280905",
  "points": [
    [
      "-1682550622615141",
      "-909450579431753561532906"
    ],
    [
      "11103423640239779",
      "1342743841352567747945574"
    ],
    [
      "12011273923554162286027898280534631/1335397569105205089",
      "-1709620633731690371275947158347993477629043038322198/1543177462540680150089633937"
    ],
    [
      "541109145531615611385249291/39835768921",
      "-13453546410506579946935553759122076567666/7950781283173469"
    ],
    [
      "28310383025192151",
      "4752774059655245831900366"
    ],
    [
      "291845636719960919574659/5938969",
      "157164407907021767306006828684586486/14473267453"
    ],
    [
      "2838220085186999",
      "-845030106720208270088946"
    ],
    [
      "88430199661220391",
      "26259162112520526606325806"
    ],
    [
      "722205914989991511/49",
      "-643777446070054253059977498/343"
    ],
    [
      "2564637586401003230919/429025",
      "-252464417191073420713520159825482/281011375"
    ],
    [
      "-69194248789413704486732027123721541084848896286383/10756494622902445717925399773845289",
      "-942303949952239829960964899470621535352017815179013602922996874000353216208/1115593940535946065843524812688882185574973976021163"
    ],
    [
      "-3687447116938960334013927893/489987400081",
      "-262881941367300386739292132167595035031846/342986770170099271"
    ],
    [
      "2459295138534263198341/4225",
      "-121954237458136796238155209617506/274625"
    ],
    [
      "870151985932050521145047784159892562271/4012267223776094534161",
      "-25660528201467872446821985505852120057553418133986530110558/254146875653888517356956526494841"
    ],
    [
      "13926388019857902457145813803037835/51678284226285253156",
      "326236011095895309261223172843478122066489900188891167/371502832435772939069281108696"
    ],
    [
      "23490564532034847",
      "-3607065627114951000813826"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 16, torsion Z/2Z. Specialization at T = −1247/882 of the rank-9 fibration of X400 with a 2-torsion point (Li, 2026), and its 2-isogeny pair.",
  "created_at": "2026-09-27 19:17:23",
  "updated_at": "2026-09-27 19:17:23"
}