{
  "id": 4011,
  "curve_key": "1538647440756859477118462623561:-1908414270572175917451212043316788646782047045",
  "ainvs": [
    "1",
    "1",
    "0",
    "-32055155015767905773301304657",
    "2208812813162227288883572183878136873046725"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 208.52536960531694,
  "faltings_height": 15.066934016917756,
  "conductor": "640259658391727630453646333422455570202860388634738",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "73",
    "157",
    "193",
    "211",
    "229",
    "277",
    "307",
    "367",
    "373",
    "421",
    "457",
    "701",
    "773",
    "1049",
    "3109",
    "5381",
    "22397"
  ],
  "discriminant": "349671761133100287884290327107470559752805552990970651191086129142650851706718292752",
  "regulator": "7192098266884369865560736.6947706830257206588363641454476681165461308",
  "points": [
    [
      "47163406358272170397323409556393273984559529/204005490695679793583686996224",
      "-246462055078564933070840907605433885377199152931929448220416480835/92143092637618869422563332087506636091322368"
    ],
    [
      "778937138912442160911142283515711999877991946/5520645421128797075259568581025",
      "-9125132231726847533204526222125791218672625519198409355345744556421/12971338158360178067919848177285519078568432625"
    ],
    [
      "530568928040982603432299931967881397404206/4332813456784332815474876449",
      "-98683010715810118910118829133593544167135072519534888600758727/285203589572140508019610797946098791536207"
    ],
    [
      "199104510056906951257769837431068855642769/856189185123136435745773824",
      "-67828677457821886839846936435568781291082103015787224640698495/25052703969217502427236832868941223047168"
    ],
    [
      "55351128993524018033972381773594478734/774825859515222404289",
      "-411801916550918594014397611937560514247559092152641111255/21567815515580679575974110693087"
    ],
    [
      "166117387661726761554554/1503345529",
      "7360110766960810795607785655105615/58289216195917"
    ],
    [
      "413489460703355133595853011/3968044080025",
      "46271957334109482640625985268792981474/7904323967189399875"
    ],
    [
      "707025019172936825286513116517256549034/6677175656392535735287729",
      "731904044521677210199843187954933487614733982342859247485/17253976494255294967738906321758700567"
    ],
    [
      "31487301854051820631415275460051/271644587649669025",
      "31846088433576622171208499869006484740101632439/141579894577451986620688625"
    ],
    [
      "147944892378962946895577913853534/1290552630221255625",
      "295495673403956855294487370574805253746911838727/1466099954955654654796453125"
    ],
    [
      "723783814079645109978476712811/6922685127155625",
      "9163817645672028964384187010680163409672909/575985920762063141296875"
    ],
    [
      "29008639033327290959311167103148999054/256465222780229573580625",
      "-22557906457530592066517434639101546475336463285263558367/129880132587787459559295628680734375"
    ],
    [
      "3053622401521179084245267627921175651694/94747553079935463515025",
      "168739326433171086339512767284596096621084982142274408564863/29164330035909846330770783151293625"
    ],
    [
      "1248131196227202572264174723387156822033156709325886/10867637490260080394353255806908141641",
      "-7359510673576069367811820378783493923942264220748977418166542893147091844589/35826362423733534943628419184112614238091705814458709189"
    ],
    [
      "16036898851239355431741429419909186057929/153061829565744601284823296",
      "39364273752473404609768827442741487475411404569754969719091/1893652782285815706800048423393003065344"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3652 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 15: 15 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 04:45:16",
  "updated_at": "2026-10-05 04:45:16"
}