{
  "id": 4021,
  "curve_key": "2339521860337726265428849265221579547425:-157253852332701209341816234815405605671453404266332583640625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-48740038757035963863101026358782907238",
    "182006773533218992289707120399188676242257095333912285092"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 272.6104233881645,
  "faltings_height": 20.739389214331776,
  "conductor": "3633958535429087440559985546561230089154484056735382962822667450",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "29",
    "37",
    "53",
    "73",
    "109",
    "131",
    "191",
    "419",
    "421",
    "443",
    "571",
    "727",
    "1097",
    "2953",
    "3529",
    "5009",
    "28751",
    "110629",
    "327499"
  ],
  "discriminant": "-6900302530841110917910003698703812679227275634052442276524987901228496789785529138216717522643475861087235531000000",
  "regulator": "3219856947640144759246385344.90301053678868591779305554683779681159337584",
  "points": [
    [
      "-1806061644291199130351251646128656/451234162206529",
      "169571714107494576465868647290473720852012503858678/9585239260517371400417"
    ],
    [
      "-86130816697293922620164875063192416/322658302431738025",
      "2559351168964353144977947901871756049562046597294345858/183279658448669124529664875"
    ],
    [
      "2979771104776188231371225424139953/422357411384896",
      "119426299583916214576557366841655796052069089858237/8680009073461223021056"
    ],
    [
      "40036354399140019906310793517552623/2260814015728324",
      "7503589192088164172282577127031214506130464455389993/107497225514502632661832"
    ],
    [
      "-447064099429231477510128369977892/53392585122529",
      "684245641885084857369282257578022336476041438558/390140847519777221167"
    ],
    [
      "239630314765492772787269858775125298/38520762373850761",
      "82660698939733090189074508718580183171255060531028368/7560357126761171104889509"
    ],
    [
      "-208070183102377858416291408185114942/27321488570521161",
      "47687126925879329700548170290885218702759075464030592/4516027067913586482284091"
    ],
    [
      "18331993965549549442591020684114976252/30922928148463762401",
      "2129223357955058377141953097572133768054838494910362991726/171957418626666522204998196399"
    ],
    [
      "-40584897028646094144327530934490462258096213/11359483026725480982693604",
      "674676496351013850662648123498905410640296204266483496778883650829/38285810942505411393579547019801239192"
    ],
    [
      "5528412851049810258724238772346249257/808635642212823616",
      "9434528205614372142728573261282907806530050034439084361/727158892818593839103281664"
    ],
    [
      "14158044262576494085261241509797650112/184621965978555889",
      "53062297279108763475821328539331011001353312301941011050/79327735488408145660047287"
    ],
    [
      "34736496674596048759591529696892225703224/2851651916558692603225",
      "5689175174279612732822611116734764779970298435162229665213898/152280666575681392502623576547875"
    ],
    [
      "-2921127335752247515430158731602110974/35474700147003094201",
      "2881758126608392588300022874458287157080585456698353701920/211289589742090159162645899949"
    ],
    [
      "768916796153252674020628143967616040297300159361638/42226105506851672028392341555201",
      "20037197560283747454650269044672770707183296694439770961602158128513766907890/274392061634147883371391469416285734444391191551"
    ],
    [
      "16404330909342087188668557948308706338982148764/2404477552449942539171120689",
      "1523815808004433428663499598976372521273877781519202317123074701569710/117904692634050371586750367484148695244887"
    ],
    [
      "252335388488401102935098954267384581848/23646744508347336649",
      "3405356604922359298541730752571492374455890079486845129018/114989196308696474067532154107"
    ],
    [
      "12664712288038146169135771222929457079639260038/4966891203718896478160779969",
      "3017444166510662512335400361398475919108967784959186531413516039540972/350047492308078712629493088781239174417953"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3485 (source contributor: Steps Unbounded). Source equation and witness provenance are credited to that entry. Exact rank 17: 17 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 04:47:27",
  "updated_at": "2026-10-05 04:47:27"
}