{
  "id": 1682,
  "curve_key": "2032575557332109768865610718259983103681113929825:-2906557586192596449987568889204326289051052060711987476910887952770820625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-42345324111085620184700223297082981326689873538",
    "3364071280315505150448571574468738762599998567472118156176194943402692"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 333.7061922328677,
  "faltings_height": 25.6241324256277,
  "conductor": "4158960092540785960398822964998502415831019202640925517818827528346583882085978524868895601057569033333947600550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "37",
    "59",
    "71",
    "89",
    "2377",
    "4861957",
    "52826660453184490529025390279973101133203797217780130812237432088688647399873759526261"
  ],
  "discriminant": "-29380060272617969719452807715373927965480283664717714736940159591758922179803489777920009707191503228156649673680023732273250937643904000000",
  "regulator": "757426742318555778338020560908.77122657122444246594571165261267588055409172974439173718913394",
  "points": [
    [
      "258026702482646468726330599764/1708249",
      "-45434739069641263933403105201025536069726838/2232681443"
    ],
    [
      "229368627554746450360076757396/1890625",
      "9149816628779748063271994644589961846154194/2599609375"
    ],
    [
      "216562276790624434256510427/676",
      "-2646727011767728881685069071169574416701/17576"
    ],
    [
      "12929265882509712101288988",
      "-46484281729898789742606681076822158378"
    ],
    [
      "-542638950477662102326717/4",
      "-650513845847760539132633134957532033/8"
    ],
    [
      "81506243768499710910582",
      "21310344281719994798195847333102984"
    ],
    [
      "152874883769436701802852",
      "21525157941050878296181328073950574"
    ],
    [
      "13747189279160064676164385848/289",
      "1611821006291040101007523052644715296452942/4913"
    ],
    [
      "2293978291034765454737604/25",
      "1980723432862716327703870335717697398/125"
    ],
    [
      "-952570816645619886090366070668/4084441",
      "-194417817714519321163058999515201718735960586/8254655261"
    ],
    [
      "53143895571486734615163768/49",
      "380900883790767195075013393993418426262/343"
    ],
    [
      "317457327733344682152396036/5041",
      "11014834196922790281231318071315998299330/357911"
    ],
    [
      "4599982594838707222947744852/52441",
      "216354958419012794474024869737318824227446/12008989"
    ],
    [
      "42356892485084629394007744/289",
      "-85957208289821584142259806009880688110/4913"
    ],
    [
      "-2813711514324297636915653844/11881",
      "-13581359912226136861249023110977927394274/1295029"
    ],
    [
      "13947730992724769230966836/121",
      "5074748557659223936643405408921002074/1331"
    ],
    [
      "614275148262185272805502",
      "457317465103362322757375961775595424"
    ],
    [
      "37542202907527679120748",
      "42746311528761252415238886185456070"
    ],
    [
      "-16651493311754478229444183342691231889570139531812/90111665965133521237977529",
      "59750705257130252109243618711229621440316490611650275747272944635825303562/855404495576705105013795867111246000083"
    ],
    [
      "332473373522701940268974114637372319032/3919364363699929",
      "4798235040957964286502683536298578972732092656562651411786/245371127939399134957283"
    ],
    [
      "952071252765520564817229334655138394660157401/9992720362110627993856",
      "13928962022053255350405791191960917427849053846564667269308604733221/998908253064940708601839223189504"
    ],
    [
      "-2208768184683282737708380216100561172188/10370615907560841",
      "55095782660781824765747830153164582918062896450096952005574/1056104333468481375021861"
    ],
    [
      "106070975227200996166924753131109194559812/2654257478722045681",
      "180155420613009170593255358965450176241974548273260079828157246/4324287642241503933890256329"
    ],
    [
      "369488625552911094084077800944526581092/3378665705416681",
      "1258943675102747168182156837709387181629214336047450786714/196389305984770276060171"
    ],
    [
      "1423588876315148064456619193290515210308330389906410409412664/6624264695647695078039476833395896209",
      "1103482785461116372148321223828564399008144109135625563429658377694151011563635385992432310/17049298591663662354566909877209744897308811043549337927"
    ],
    [
      "176575560540650477568115633132231720272441488705581970131258641194532/1130990418886962607290890713850190378577514041",
      "898834710585683006216314663083645742759228877616983255933448923928859303201351528454083992896078331786/38035435109290740640620582526870857525027062300945049339969468152339"
    ],
    [
      "25092516108957056266532374025546160678/238972116790729",
      "32082204405897470973297913674691205944714980132162055128/3694203758191528579067"
    ]
  ],
  "submitter": "Ritik Jain",
  "history": [],
  "commentary": null,
  "created_at": "2026-09-25 04:08:47",
  "updated_at": "2026-09-25 04:08:47"
}