{
  "id": 728,
  "curve_key": "129373078638267133260964906609554276715040678205605521:-50173037652165255876331330338774386328247149807490655628418152841923449241824569",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2695272471630565276270102221032380764896680795950115",
    "58070645430746823930939039519345796725516724439864925595007798344169481404417"
  ],
  "rank_lower_bound": 29,
  "torsion": [],
  "naive_height": 367.0342300747634,
  "faltings_height": 28.543003378100185,
  "conductor": "373311163292677499812856331134685180923731435354851746325416047107220696523044284065917244788194219682890915991886062890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "37",
    "41",
    "47",
    "53",
    "61",
    "71",
    "83",
    "230356944105531027122959977046222329093333893244114716488245495013109908196343024498561458924446725619"
  ],
  "discriminant": "-203683787517950029015641023933573057569787662504242280824650680870198148366064409224537444616773975121893041403858152661840353838880789692513043986278400000",
  "regulator": "105924260477161814835722637714334.949314847667879625172769483442393999499957052771794895459192747",
  "points": [
    [
      "418228045847034807466938119/100",
      "-216498069910260140225513788388659900580167/1000"
    ],
    [
      "296583835070036242594215067407013376276/1346567613889",
      "-4977994223129867221543962105171066278555666635678559682941/1562579950806231713"
    ],
    [
      "-7456595017152713971258998838/361",
      "-2221829304696731408903281829987016400116553/6859"
    ],
    [
      "445839830719056887104704050463406356574751169858157765195610330588465940254/11263257399577928892691333873534224611666087139241",
      "4376360753220120740920948316647695290546000574987858748672812820986970660477583104118821365621738999805106894563/37800366771852464300077018301857452323992163396256373292729439795761215211"
    ],
    [
      "145498066503447182598788658062/3721",
      "25342206394972379599412294660978851733419805/226981"
    ],
    [
      "-77053846024127683664568034/25",
      "32197780004063811684894325729457304916549/125"
    ],
    [
      "195827869811800141122678815145831017301023100334/564148886284765950921",
      "-85744734567535592425784974724874054135355926440555506942853767696605283/13399562004222151060599669470469"
    ],
    [
      "148227069854399566677736939872871761038/4588965142969",
      "674795440335802360674712300120803601527504671936054551739/9830421472721333203"
    ],
    [
      "22294131232137657868159104242/841",
      "-1767187328048226187641898101614956063401995/24389"
    ],
    [
      "412197937120441937269620808526/49",
      "264636943195775605846027024015885387502949359/343"
    ],
    [
      "120714844111282213322688243748471960217742074/30963174095946481",
      "-1326180752204473605797430814515050204331603235376586842870984472713/5448390311859350270285879"
    ],
    [
      "630823876550428613256184106/25",
      "9784258532578550643656524163413272080689/125"
    ],
    [
      "-1436578199039549869592898001843185778/23907035161",
      "204298529249183561905385003911441910362408483269901867/3696481869558659"
    ],
    [
      "235602940633417491671513942",
      "3535686669914432079910731241224869289425"
    ],
    [
      "919022722796371359277760566835850464740586/5031421967955289",
      "-849058000476237061595334676536224887828249606449949137272208931/356891424276161992232413"
    ],
    [
      "-206167132815886509744701983050653357374/5728713001729",
      "-4515615756346322657777560864313777788267365005642702081359/13711519894387314817"
    ],
    [
      "-6403214093940613819431024195593254016/251471157961",
      "41860603869166272003825986469090745610734644019631050747/126104990111544709"
    ],
    [
      "-419666408329073174770069778368574494/21341411569",
      "1002852063632863611846551402044164092311185360316550539/3117702791880503"
    ],
    [
      "9208334135100011428405039127060719166/255513063289",
      "11365157557068600541440215697352603371488362538220627371/129157509770513587"
    ],
    [
      "10346670051343068194847404251444845159368029838/554730251081025776761",
      "1561732161579154401957318800553559317233452926282973294283812462508981/13065401941805264230293791425741"
    ],
    [
      "114036816367547089005563694647919168151614379/3165451276229052196",
      "495069706908325240012771870188282491481811063253821717720501886047/5631880739621675006342344744"
    ],
    [
      "150957311350027199526385164291294535622/938482375009",
      "1769090086961785421961089041747062803527272246601373550097/909157616237093777"
    ],
    [
      "28790391557987780963450314638312468536954/140048739339961",
      "4743575070381672842110359123057132694385677278818991400607347/1657367452023013925459"
    ],
    [
      "6463835327871789700300635836800388629967/720437673796",
      "-519670629830195818574192844491013012742723295077794799053347/611497411390611656"
    ],
    [
      "5963891951007101872456053200996694480544346/165489570081552649",
      "-5923618503905141394697582533792196642705795756101383034346008379/67321834457985961408192357"
    ],
    [
      "10622300491019295346894196077209892659217223504/32979904816883795761",
      "1081430462927195464015588322128080645294815313020459119559678498738777/189397436641752518371546540759"
    ],
    [
      "587013129845936723406815874975873042749/2239584082576",
      "13963960503363394832809215202310375542169300676753727722437/3351591329592965824"
    ],
    [
      "54108091759208421579831463712316274742332604146961760836/1431658306561277346535895776489",
      "172919964109868089540969558096251369812355429121563820295047542140283044092703236669/1713006717803165136761304003496736382423793013"
    ],
    [
      "166353119525545432673001793653695329358782/4277221345419961",
      "-30738930356112292854354814405301962582809670016231634144927563/279732282007276451361709"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "Specialization at T = 20920/2293 of the rank-17 fibration of X1092 given by:\r\ny^2 + (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pE + qD + pq(L-p-q),\r\nL = 33259T^2 + 122264T - 682370,\r\np = 95175T^2 + 2786613T - 32668,\r\nq = 1936T^2 - 62631T + 606464,\r\nD = 7(133750152T^4 + 585493575T^3 - 46370601212T^2 + 50749834445T - 26401212000),\r\nE = 217588848T^4 - 1500919481T^3 - 129911904187T^2 + 1875481523886T + 337787445024.",
  "created_at": "2026-09-14 00:43:54",
  "updated_at": "2026-09-14 00:43:54"
}