{
  "id": 4014,
  "curve_key": "16272499307592628459809973191490561:-124373014175157657214306623726971679249074009798269441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-339010402241513092912707774822720",
    "143950247887913955080900318015720759906665567142400"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 244.51024994323345,
  "faltings_height": 18.433569803461335,
  "conductor": "4657372890037610572108520563138067741151339367609178987970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "31",
    "37",
    "43",
    "59",
    "79",
    "103",
    "113",
    "257",
    "271",
    "601",
    "1051",
    "2797",
    "4919",
    "81013",
    "270071",
    "599413",
    "1520587"
  ],
  "discriminant": "-8949269554993736037631396937806297885050382040469746006255730503512388623128990159197766871477785408000",
  "regulator": "72258173110877537981025435.70626995111873144675091127590801776793230679",
  "points": [
    [
      "-4160661923033059697616872127720/648247804625521",
      "199334399701165889050293375363376990965696075840/16504850009954853405431"
    ],
    [
      "43451779200604365037878984/3504995209",
      "2469697187985831673138023932714885452224/207506231358427"
    ],
    [
      "116188432557910647302599830/16992947449",
      "26392086914717720427963348369023513164950/2215149650609293"
    ],
    [
      "-13688041883739600779980385977113999/307385554849293376",
      "1433407899900241739686118253551076156789681646418283/170421813284796007361114624"
    ],
    [
      "2300055219250084118238551554189162989/431914074482890000",
      "3488229132816123965836326171042565219353993330486250587/283854664004081928913000000"
    ],
    [
      "17031765173994203125513287097675787880/738903454645605806881",
      "244665709437184724044401031051840092115164871814853272640/20085449044701685751790417628721"
    ],
    [
      "-31097569985432227092682500/646227241",
      "114792795269932588244332407954201846480/16427742693461"
    ],
    [
      "278858110027449129800863747545963155/284667370950105796",
      "147241913752751061743805119121146781271529523225928465/151882079846329438339689656"
    ],
    [
      "-5834318724337729913346551912253852/184840383586232929",
      "882078561069301073038840663102801463176582156383504/79468550512807276699731217"
    ],
    [
      "63831695052774666708240771619902943950/2505607724034948297241",
      "1545515623216645979622148906999980497480479609826437770270/125420815063789756764341010257789"
    ],
    [
      "53675442042337085311768406385274320/408019988090522929",
      "12703959361621183384120601589281023098659915472328560/260628652265109750510954967"
    ],
    [
      "3540139462577196624924285185413619052/80514791111117978521",
      "10569840098808796599071371619187073487622272966353096656/722459499301753656848256661181"
    ],
    [
      "10283923857917664524455771306770777180/214811372621863894009",
      "48514055956742044849220424675698959183284806863558718640/3148371013859576686697172820723"
    ],
    [
      "3518036245016965105949726695579824/454710678912088225",
      "3651121490968426864824260270995554320402320475139312/306621589488968537212416625"
    ],
    [
      "-7420351521442584873313995197239275/963559236533323024",
      "11432706582532843892504542717795629682444184124386685/945839894786989049316488768"
    ],
    [
      "-105726559615073702798739295316730730500/1943889121196378477521",
      "104809336409693733197792018849455061514546298885455256080/85705212078745082547955065094681"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3655 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 16: 16 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:46:07",
  "updated_at": "2026-10-05 04:46:07"
}