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Label Polynomial Discriminant Galois group Class group
34.0.11627528865280854983574434471375691019078604726189023.1 x34 - x + 1 \( -\,83\cdot 1291\cdot 12973\cdot 4134484433\cdot 64200532307\cdot 31512487292285521887257 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.2.11885748945456377039253666531245020090157279092950049.1 x34 - x - 1 \( 7\cdot 191\cdot 607\cdot 14645575916792712592989131451003587034531413111 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.0.770483087302237618924031213653875461627441440985549111296.1 x34 - 2x17 + 2 \( -\,2^{50}\cdot 17^{34} \) 34T9 Trivial (GRH)
34.0.3804212187770006845104225428814283599364285631706866468067.1 x34 - 3x17 + 3 \( -\,3^{33}\cdot 17^{34} \) 34T9 Trivial (GRH)
34.2.2218093599048730338422311977952739821538878416469987145298721.1 x34 - 4x - 1 \( 151163\cdot 3136253\cdot 9671606647\cdot 432210572699\cdot 6906809950567\cdot 162051016270589 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.2.2218093610805369243106601538481015288800287251162174144380928.1 x34 - 2x - 1 \( 2^{35}\cdot 307\cdot 135071166289\cdot 1556786286410745966442476272513982827 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.0.48276286010390714256067324090953417465726070579884714323083264.1 x34 - 4x + 4 \( -\,2^{34}\cdot 41\cdot 131\cdot 149\cdot 2536801\cdot 1384159628151677292063543432530712442649 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.2.52712473208488174931543295145087347040705933972973178792706048.1 x34 - 4x - 4 \( 2^{34}\cdot 1459\cdot 2074583276749091\cdot 12353611446652867\cdot 82056584977043939 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.0.98770665619830158849872633708973799718942072856313660880977920.1 x34 - 2x + 2 \( -\,2^{34}\cdot 5\cdot 4463\cdot 4597\cdot 1786284823\cdot 13682879113045277\cdot 2293023653476192171 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.0.100988759218749779147522858208201148476497340017318555932408799.1 x34 - x + 2 \( -\,13\cdot 1061\cdot 192313073533859878065118129\cdot 38071982428796861661094741190767 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.0.100988759218878889187610619236040764506432004552857893115789312.1 x34 + 2 \( -\,2^{67}\cdot 17^{34} \) 34T9 Trivial (GRH)
34.2.100988759218878889187610619236040764506432004552857893115789312.1 x34 - 2 \( 2^{67}\cdot 17^{34} \) 34T9 Trivial (GRH)
34.2.103206852817927619525348604763107729293921936249402125350600704.1 x34 - 2x - 2 \( 2^{34}\cdot 371237\cdot 768749632105135909\cdot 21050019716166134869652117257 \) $S_{34}$ (as 34T115) Trivial (GRH)
34.2.79666084014551601611187998196780089112851885147392749786376953125.1 x34 - 5 \( 5^{33}\cdot 17^{34} \) 34T9 Trivial (GRH)
34.2.2153191597794813561044627373563437161207987263698064185878442600361.1 x34 - 3x + 1 \( 197\cdot 10929906587790931781952423216058056655878107937553625309027627413 \) $S_{34}$ (as 34T115) n/a
34.2.2153191597794837074322438110795459989308989884409173421762261739433.1 x34 - 3x - 1 \( 244429\cdot 1673257207\cdot 38358820791399678810111461\cdot 137246726042042407050370751 \) $S_{34}$ (as 34T115) n/a
34.2.2153292586554044196572720352798684616022995006058171661713467959209.1 x34 - 3x - 2 \( 313\cdot 4493\cdot 100109\cdot 401951069061523\cdot 38051867672147091984640640128379538771443 \) $S_{34}$ (as 34T115) n/a
34.0.2652335238355663972863781109929452800183143879582476922663961790823.1 x34 - x33 + 2x32 + 64x31 - 57x30 + 107x29 + 1603x28 - 1261x27 + 2206x26 + 20286x25 - 13891x24 + 22349x23 + 140429x22 - 82189x21 + 120996x20 + 538574x19 - 264119x18 + 327327x17 + 1143572x16 - 499882x15 + 128724x14 + 1425880x13 - 737516x12 - 1133952x11 + 1294431x10 - 1061173x9 - 1305757x8 + 907693x7 - 16051x6 - 713165x5 + 590348x4 + 474529x3 + 129602x2 - 93135x + 56857 \( -\,103^{33} \) $C_{34}$ (as 34T1) $[5105]$ (GRH)
34.2.2700362373274479503814347058194205801720543251535535494390701020689.1 x34 - 3x - 3 \( 3^{33}\cdot 37\cdot 59\cdot 1637\cdot 14076649\cdot 88307993\cdot 109350036125618252414991335369 \) $S_{34}$ (as 34T115) n/a
34.0.63202676136272336959991610970496247892496604140281149752126821177431.1 x34 - 3x + 3 \( -\,3^{33}\cdot 271\cdot 41953168948728165785591152809986575453874281769107 \) $S_{34}$ (as 34T115) n/a
34.0.65355865515973563228944805974690169400790305224403072011714938535936.1 x34 - 2x + 3 \( -\,2^{35}\cdot 3^{33}\cdot 269\cdot 2747421509655671\cdot 462973083335522483486401 \) $S_{34}$ (as 34T115) n/a
34.0.65355867734067162148565103624914668628139062779670233016609989966815.1 x34 - x + 3 \( -\,3^{33}\cdot 5\cdot 7\cdot 89\cdot 97\cdot 397\cdot 98008307039509398113133304615102149422418683 \) $S_{34}$ (as 34T115) n/a
34.2.65355867734067162277675143712675696467755092714334768555947173347328.1 x34 - 3 \( 2^{34}\cdot 3^{33}\cdot 17^{34} \) 34T9 Trivial (GRH)
34.2.65355867734067162406785183800436724307371122648999304095284356727841.1 x34 - x - 3 \( 3^{34}\cdot 1607\cdot 11167313250696079\cdot 218372199975176439296976826510513 \) $S_{34}$ (as 34T115) n/a
34.34.32492169951483601485711825975325195410331229243708069666036144501372297.1 x34 - x33 - 66x32 + 61x31 + 1891x30 - 1607x29 - 31023x28 + 24095x27 + 323844x26 - 228291x25 - 2262360x24 + 1435905x23 + 10839684x22 - 6136823x21 - 35945371x20 + 17958849x19 + 82324817x18 - 35828109x17 - 128721615x16 + 47931532x15 + 134553261x14 - 41728477x13 - 91025976x12 + 22664245x11 + 37938129x10 - 7334043x9 - 9042178x8 + 1347387x7 + 1118049x6 - 116296x5 - 61867x4 + 1806x3 + 1328x2 + 77x + 1 \( 137^{33} \) $C_{34}$ (as 34T1) Trivial (GRH)
34.2.38106557768536174824751840635085127020970621757293090110917792357154816.1 x34 - 4x + 2 \( 2^{67}\cdot 19\cdot 211\cdot 63823\cdot 963227\cdot 1047726894655637300780835628081202773 \) $S_{34}$ (as 34T115) n/a
34.2.38106557869524934031874090917327130245597335762414739109157743563374592.1 x34 - 4x + 1 \( 2^{34}\cdot 40031\cdot 890177\cdot 992441\cdot 3833841872344077247\cdot 16359429946447811440468087 \) $S_{34}$ (as 34T115) n/a
34.2.38106557970513693262509619010306365493052150770157099216633578588733440.1 x34 - 4x - 2 \( 2^{67}\cdot 5\cdot 109\cdot 10313\cdot 16961790757\cdot 2708549590060364354776124532170959 \) $S_{34}$ (as 34T115) n/a
34.2.38171913737259001205908404966408421953479141356439429432331632646291456.1 x34 - 4x - 3 \( 2^{34}\cdot 3^{34}\cdot 47\cdot 181\cdot 6659\cdot 2351884408240028088566983947451527547 \) $S_{34}$ (as 34T115) n/a
34.0.216871709053797144023035626416117297657214779404251394209753260074467328.1 x34 - 2x + 4 \( -\,2^{32}\cdot 50494379609310334553717548590180766223281337740889609374514143 \) $S_{34}$ (as 34T115) n/a
34.2.216871709054906190822559991584986290420748261797996360058025376191873024.1 x34 - 2x - 4 \( 2^{32}\cdot 29\cdot 719\cdot 9021071\cdot 501803421221301371189\cdot 534963847310065662766809302401 \) $S_{34}$ (as 34T115) n/a
34.0.867486836217406669691062125962119415128086466374560844000017935349300191.1 x34 - x + 4 \( -\,463\cdot 14791637311627073\cdot 19252730983707458016119\cdot 6579203357365186253381357900311 \) $S_{34}$ (as 34T115) n/a
34.2.867486836217406669691320346042294937183765698434430173071096609716061217.1 x34 - x - 4 \( 7\cdot 59\cdot 71\cdot 29583836449797315066375212155724002905015370133834538521675701998979 \) $S_{34}$ (as 34T115) n/a
34.0.3325466068076643664357827857598159738994734276327509143073421552355865283.1 x34 - x33 + 49x32 - 162x31 + 1646x30 - 6093x29 + 37764x28 - 140505x27 + 642029x26 - 2158868x25 + 7867204x24 - 23451724x23 + 70989641x22 - 182710441x21 + 459461291x20 - 1006591547x19 + 2135502310x18 - 4017190895x17 + 7274499825x16 - 11714663796x15 + 18043531688x14 - 24702818067x13 + 32221074210x12 - 36915149197x11 + 39648896356x10 - 36487346558x9 + 31372407145x8 - 23064375767x7 + 16052201854x6 - 9172737675x5 + 4518648355x4 - 1618857168x3 + 448908855x2 - 73089631x + 8048569 \( -\,3^{17}\cdot 103^{32} \) $C_{34}$ (as 34T1) n/a
34.2.8350207664850893587674765141294032045697120106790441256127699394134602033.1 x34 - 5x + 3 \( 3^{31}\cdot 2879\cdot 451547\cdot 77705103841531489\cdot 133827143657449261027156958311927 \) $S_{34}$ (as 34T115) n/a
34.2.75151934339424787597016285057602390467734507951700253635364992601268976313.1 x34 - 5x + 2 \( 540448112458718370989\cdot 1120554565382189936398951\cdot 124094676051448783765146935867 \) $S_{34}$ (as 34T115) n/a
34.2.75151934339525776356246920585695369702981962766707995995472468436294335161.1 x34 - 5x - 1 \( 37\cdot 31751\cdot 416341358907437\cdot 153649614853535659350642494630254098797266015157328319 \) $S_{34}$ (as 34T115) n/a
34.2.75151934339626765115454042835977611706206589480713117644470708387500554937.1 x34 - 5x - 2 \( 13\cdot 53\cdot 5007441207247\cdot 21782367581944279061960109090017813346586751837340528217639 \) $S_{34}$ (as 34T115) n/a
34.2.75151999695393510423397441621933713762667016471299399974686406441558112953.1 x34 - 5x - 3 \( 3^{34}\cdot 71\cdot 6977\cdot 16831387\cdot 233804957\cdot 551519538743363\cdot 4191372752126305286083 \) $S_{34}$ (as 34T115) n/a
34.2.76019421175743183025926355182792208263126474798611181148453407766917446329.1 x34 - 5x - 4 \( 41\cdot 35376678400421\cdot 24812344311226982363792027279\cdot 2112301216453968412040270714291 \) $S_{34}$ (as 34T115) n/a
34.34.342523005011894297428856269332610453116457630461733441736562419892654124149.1 x34 - x33 - 101x32 - 39x31 + 4475x30 + 7317x29 - 107886x28 - 308922x27 + 1428035x26 + 6473545x25 - 8038724x24 - 76649821x23 - 34999669x22 + 511384499x21 + 872682200x20 - 1610027003x19 - 5837837426x18 - 597495179x17 + 18112177824x16 + 20594193249x15 - 20555590855x14 - 57678181587x13 - 18084925848x12 + 57474448334x11 + 58215655753x10 - 9898232087x9 - 42024711035x8 - 14514531077x7 + 10323419848x6 + 7567081746x5 - 122533277x4 - 1123034742x3 - 160716846x2 + 51273995x + 10497967 \( 3^{17}\cdot 103^{33} \) $C_{34}$ (as 34T1) n/a
34.0.442395848806444333196713449710663325979115564010458272524910178228286521344.1 x34 + 97x32 + 4040x30 + 96737x28 + 1499007x26 + 15996211x24 + 121823703x22 + 675554879x20 + 2752450407x18 + 8237696660x16 + 17941689717x14 + 27884282812x12 + 29930432911x10 + 21101216892x8 + 9069664015x6 + 2134903778x4 + 234085541x2 + 8048569 \( -\,2^{34}\cdot 103^{32} \) $C_{34}$ (as 34T1) n/a
34.0.1293500967432024291741658275904719819887687451283793314360082149505615234375.1 x34 - 5x + 5 \( -\,5^{33}\cdot 619\cdot 38671351\cdot 12202943359261453\cdot 38037505283446249225037203 \) $S_{34}$ (as 34T115) n/a
34.0.1368614795213680543163849809121687125228400988613736274905336224314527055872.1 x34 - 4x + 5 \( -\,2^{34}\cdot 547\cdot 145637780477061339818739049746349217820958674982991235016713239 \) $S_{34}$ (as 34T115) n/a
34.0.1368652899618358470303068122167977078795209424741511425946381196179647830103.1 x34 - 3x + 5 \( -\,373\cdot 3669310722837422172394284509833718709906727680272148595030512590293962011 \) $S_{34}$ (as 34T115) n/a
34.0.1368652901771550068097893439851509820974658000000000000000000000000000000000.1 x34 + 5 \( -\,2^{34}\cdot 5^{33}\cdot 17^{34} \) 34T9 n/a
34.2.1368652901771550068097893568961549908735685839616029934664535539337183380513.1 x34 - x - 5 \( 176357\cdot 7760695077436960642888536145214252389957222223195166251776428150496909 \) $S_{34}$ (as 34T115) n/a
34.2.1368652901771552286191492488581847558960185066964787489931696544232234811392.1 x34 - 2x - 5 \( 2^{35}\cdot 149309\cdot 2514616468092439\cdot 106092756187731006661249442273067667119230969 \) $S_{34}$ (as 34T115) n/a
34.2.1368652903924741665892718757535042563154106575258488574053618803820352169897.1 x34 - 3x - 5 \( 79\cdot 49002700382722932199\cdot 353546236585628524139665041001153658455181150960181857 \) $S_{34}$ (as 34T115) n/a
34.2.1443804836111075844454128603798299822061628548716206685639917850494384765625.1 x34 - 5x - 5 \( 5^{33}\cdot 13\cdot 2464393\cdot 725338571\cdot 533708669998927768669222507438011059 \) $S_{34}$ (as 34T115) n/a

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