{
  "id": 4009,
  "curve_key": "305896410291602431916269831174801:-5350033763512578440471018291669376611048913382201",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6372841881075050664922288149475",
    "6192168707769187478734262562807556408152970625"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 224.40239791800371,
  "faltings_height": 16.33264033852639,
  "conductor": "177599378108948787912335962451915637757725844372530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "53",
    "59",
    "71",
    "73",
    "83",
    "107",
    "127",
    "463",
    "1069",
    "1231",
    "2879",
    "5547599",
    "16379591",
    "16791659"
  ],
  "discriminant": "385070171935294653403724369825095963123593324453895990406239700940966689255248487299680000",
  "regulator": "2071941150628864249119799.8038575983208870939563849383440274638655127",
  "points": [
    [
      "282780299513268473649316578734439161081235519512684390/57708545901173672410092564446960152249",
      "-133420193233478310756229640344776457944296379665974618336800879083304365993333125/438389553927203774772394394832307868316330644047859700307"
    ],
    [
      "358595590609508951658163353967620737283986/89123025448410593563491481",
      "-179843771179779774767371938979473714164086925299299995313710777/841365851878526515483692197623424893379"
    ],
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      "35645657570558281988332248735293657366/21149821002469161499225",
      "-47536755406838789070519581459174469511212786707325189181/3075813822090663229394547792755875"
    ],
    [
      "983407432099957066760258376133910/562601859110817409",
      "-8369445896301330324166219178690816343788399674105/421989596687152258584523327"
    ],
    [
      "114993157533636145203301391120/48107444018209",
      "-22671606437977421666509125606760451017593775/333670970660428768177"
    ],
    [
      "43328422644897540464558916106219729/23952603207350502400",
      "-2831355256738170609341525730577632708984623024673143/117227385796389361463775232000"
    ],
    [
      "1614440378231709318601617400/866103838609",
      "22651770260424911414589372508307628430775/806036939089950023"
    ],
    [
      "5318679503719681136170449660603298/3544770581038868769",
      "-18957784798791141323916399267742648854425383470943/6673938480633492065439534897"
    ],
    [
      "124375489344633103192029112868/85085920985209",
      "-69802065278515356943183484986527770303671/784849807609527813427"
    ],
    [
      "365428272827768214236321196381076/247555764671157121",
      "148625600790764074609675289031069325159659610147/123171311546306469146998081"
    ],
    [
      "3068653679612883623053762919517653150/2089401598475288733769",
      "-65920620643393750999275466290345871525491529943111075/95506489894009508941255367878853"
    ],
    [
      "3208599949828481668365954216710/2190738822798241",
      "-39791861958087127294008327248252186063759215/102538251354144370626289"
    ],
    [
      "354206342430506524680011952983900800/195890558773539723921",
      "66075110584000948055723801366251931350344315626293625/2741702055096930405573297259719"
    ],
    [
      "73451827978080570844789033988928346/16710823157981291641",
      "17159961127774776425320918859652118696109268367099667/68311962946526059953511765811"
    ],
    [
      "112700819835830192549431611484632504595049596790/76774321591156531537591589437729",
      "-429375052999291300902385638378654511952178570643911699664619839866625/672703955429018044473844666818658140861177343183"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3649 (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 04:44:55",
  "updated_at": "2026-10-05 04:44:55"
}