{
  "id": 3842,
  "curve_key": "3976130757301965266021581892032861931321390278420668143264001:-9241735031392294358695612142623770688082042922936071077919342134533073667197804866894885249",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-82836057443790943042116289417351290235862297467097252984667",
    "10696452582629970322564365905835258421863312229899500227353576404194467503993863279559691"
  ],
  "rank_lower_bound": 31,
  "torsion": [],
  "naive_height": 418.9127760229012,
  "faltings_height": 32.899110944424045,
  "conductor": "458138337944676485250073818768314335580111441134346462258564095439541094398159795793404040938140237553397470869127504806702607453569937136772570",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "19",
    "43",
    "47",
    "83",
    "137",
    "139",
    "229",
    "8677",
    "1462259686981933325833",
    "2973132515675943288998857",
    "83425533362682707411646761992927",
    "95124777434204066868600976857622097160234787"
  ],
  "discriminant": "-13048939091600481240109365793385368933581331338721440739022332884153254067038447722553560350455625371369101409553381553294409382805918752589090453707151203446710395046025120000000",
  "regulator": "19999704993451064104189764540473240677.99267047821532833497384924367438227554823653641121922639046809",
  "points": [
    [
      "243308398617909525293298402511",
      "-70323199247725912965036903090982117873347866"
    ],
    [
      "-2052560722112939075859789979063829/9025",
      "114298525605736847590451254279843312939609419853446/857375"
    ],
    [
      "968611126910151883540172373311",
      "-916088840769069467382822456296532896327022346"
    ],
    [
      "-46190249516479225613305812949",
      "120100466440435533109676791957626455352400154"
    ],
    [
      "1247985792950009427038413689028315/6241",
      "22743832098889436775280474557153896021805095523478/493039"
    ],
    [
      "2316453651584035157140700407171",
      "3499828918124002907543725011006089730162101314"
    ],
    [
      "863260689259440708829457644079",
      "-763220560086430427299614716860022387606104954"
    ],
    [
      "49724444667980628804644476511070035/247009",
      "-5730320665357771321982750345539379429298577190368334/122763473"
    ],
    [
      "-88737106510050679170565862104269/361",
      "873169776166646490501167865000652830602886212526/6859"
    ],
    [
      "8719847439536040195754490741644811/38809",
      "-447588626292440140574707910001831344886860094958598/7645373"
    ],
    [
      "81628371180610768104851555036465/256",
      "-529360560681818046003255887269570958754095135423/4096"
    ],
    [
      "468321947735055238825914600701",
      "-273161910262910444948468572798398293569951306"
    ],
    [
      "-3321318450067819643289254446049/81",
      "86330702030921062715078081759240099086000811606/729"
    ],
    [
      "227770453256847629395168398511",
      "-60377446020777769313199312127271125641841146"
    ],
    [
      "72743421248906081909427590520409",
      "-620422002257165056623998137816381676037112282874"
    ],
    [
      "116816693654735247829477491158728771/961",
      "39926031847714350251457029795821137118701987201801214/29791"
    ],
    [
      "17648039531132585552122794138048724029088012224869211924874782362168752633261/116276395475164578964001059216737753495285855201",
      "1595970271803418158492964374114448762990189668088830951525078261254612149940586030771112276181481934699968238887484/39649465808862432382177857599337859253415592156592601336289724503422801"
    ],
    [
      "35594283527836156849142008036103789361270808108750811738520148117299/201782064203857724868699815584950323929",
      "113688310108809467621954503517474354895821873002669206028759937661147169836798323415850868271901504402/2866314500461239046621097547201069939052852916543741685533"
    ],
    [
      "-6305593297169823613087365541281439526147581412757687390328274419/23677658050492504126889018110137241",
      "429081298776945681769769433153454689970303328001665502306908213953049929680067703882822219714014/3643410590430299028556721474212959486997925114358461"
    ],
    [
      "896219072219447915479973856718262724799022940359909383700292641060827919699557339/5459570933368721116313075919000625726065172774590841",
      "15737636577809891583679010333767763903094716326488524059711088218041447647926123387272972290468523347804189164985876294286/403401742097247270045031090401894273947229230549643370476533455252285497033139"
    ],
    [
      "58123834737645910863921536600515944437874898942852995495822333320923960381423708089197499500019714731574341908635687091429/681467340685213758868063402460379193273702931377211064903196220052707845582888124185669886449",
      "1159970817702887782137798748206607888067513071504187683576417437328781573560025568178713987237823093012485919867078637673378695188501471710917503666988038341387052058420805386203865652/17789656839263751839806993942131664812473038848701644060754606126750565924985393393236751344719332970338489774336088694425736493626676318793"
    ],
    [
      "-1898123269985721942323036256970054841/6365529",
      "1513713354498314841538421526280203969687996600530711938/16060229667"
    ],
    [
      "36644167941088976709884737912040665402116487630338406653432046491/464630638689842694278415386554545796",
      "21605923403896659575129777451701174134149388561224957794952428272926338132486720253794472203104941/316709993240649256052970337974562727076275103535550344"
    ],
    [
      "-82441233442689705223473555862715451869613064825481442758582698581/467651290684986791358148297139193025",
      "45024055134775352279104261330722337742806442875165389164941410346972006055510615531291695838025082/319803495219200026138614837867627648498906570134158625"
    ],
    [
      "-35606431015887777480206651322982950995015103312988853830324982337269350644895889338532945955951144367085274673640277892338686997323753159/157617406777216361472631227455534069895777972226665914576717944430072177946219092165286866638252238468311296",
      "8367615871241241540247819513690502325296936298482465910445430507395583513841893466871112373701198140434400878108346310918088130153122762361798405658784515839913729065418890610091563690334711486129831529909/62575779302589215007826239953515069645709459546963059650132146094130915145550607874473920511289149880442860116073895663741407758441019380328081923184814201286656"
    ],
    [
      "-16831936808025670360389078464052785214211841940326384345788234057372681156776850968330590611204529669/219066648663293385648205660882732609752121242964848894824832176441299161",
      "13213475886026970587147207606150463719009650866142215246663614513472557152192434602533152458989671983458225926324188300400014684233534298478231090083474/102533172819043378960818117666961983176163115689052005775681774441783559521895796056315648249476503938317341"
    ],
    [
      "-594893092735450343709128006070949754525138015596443551892202873453432910893270119696100679/2912607498331771087438437661426359822511131267080529756750625",
      "686881297022002485666387975826751140548165291053543933449109174501566082325574361424540462274190920448684243161755678221078759500047456/4970761716606764739454572081141384516993528278593423286502524578006465956093116623047640625"
    ],
    [
      "2575633519917358062461638812810943906227593272696388812979522953369786824318853014909/6839236728647173431054991035295511289063491491395210289",
      "3244780199946279564458728050199816367607088581357741984995898571684888835741057587199056290606994086418483461242188398851705178/17885927027401943582226278797774568502263750367609928822495808567115541356684640087"
    ],
    [
      "-2575129677479650659336122083886760057820457841362719961471215288486397445232577170789300028674351097101911682606934254065550619715775538139342277061861/8472944823904845265592462173506329507075512390391163253681052795270066835948549387722499505400858880023387141284050608209",
      "2178059939797920205412898753757966530627184329671419132610400069224190046472971506106254627046160050655570204637350783184449209039751116579701208832225130532445331021159868147595741066602542046536001633099206501548991963112822/24663321680839618656669161548624323828331769754266085693875392006177259113306109530378743694441699760934817613529412737877152728125289430947307545629184332273432175727494876338326823"
    ],
    [
      "2733043343510870144371490223726838356085112191657433951853609139334091548898439/25255109861976615757237863955434974596095966830209",
      "6950996311254539748619286998534782085025622411955412119988077855034648941294729506132382664495466330560749839189852078/126918196773148112041689977141359712137514431344166194646117087129336522177"
    ],
    [
      "-621206320450480453134024121744286408723177833801156660905487612427052598126333311524651825838800867819816418095880047700849422079790949/3560957249434388558040513028862170171458944155663144495502161655568989301455934934690994366298793020183681",
      "29929629855146853930701401750476584498751419006549586335198182233501658908738963339880520226421956162913958573984624956384634242528958073369745585002938610647945049592634267451222105005164019651366623994/212495696842404213466277508006936136078274401130382777604797227609165969328559334859209624506173246103334909267017370491300793453204640096838073059704202761921"
    ]
  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-03 18:01:08"
    }
  ],
  "commentary": "Specialization at T = 45003/19591 of the rank-16 fibration of X1092 given by:\r\ny^2 - (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pq(L+p+q) - pE - qD,\r\nL = 1538155T^2 - 92214T - 63843,\r\np = 377221T + 81663,\r\nq = 8700377T^2 + 2639207T + 192390,\r\nD = 4352378645285T^3 + 2047910533662T^2 + 307043378497T + 14459329500,\r\nE = 7(367337640432T^4 + 81245875297T^3 + 20123774463T^2 + 5809845488T + 479378460).",
  "created_at": "2026-10-03 16:50:04",
  "updated_at": "2026-10-03 18:01:07"
}