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Label Polynomial Discriminant Galois group Class group
38.2.1086466936935771765474507582942119612061614764913786264052821.1 x38 - x - 1 \( 624808693\cdot 1738879354765590249997542180390437704844184626147297 \) $S_{38}$ (as 38T76) Trivial (GRH)
38.0.282043823418243542433249166060715711952450320814680588841203531776.1 x38 - 2x19 + 2 \( -\,2^{56}\cdot 19^{38} \) 38T9 Trivial (GRH)
38.0.1762476198890992238387926942683405611628934289942221754009257333083.1 x38 - 3x19 + 3 \( -\,3^{37}\cdot 19^{38} \) 38T9 Trivial (GRH)
38.2.2901373404155647104441523981239181159929184708380460029220825235930489.1 x38 - 4x - 1 \( 11149\cdot 365159\cdot 14342233\cdot 49689992079559593586453718567433043366296684203166163 \) $S_{38}$ (as 38T76) n/a
38.2.2901373405231558906417603818965707338993499524889151117093324667748352.1 x38 - 2x - 1 \( 2^{39}\cdot 199\cdot 28308359\cdot 2683125188231\cdot 180622253751001441\cdot 1933097818431428689 \) $S_{38}$ (as 38T76) n/a
38.0.7892746960221820898131562172323886834213973461541107170325061114527744.1 x38 - 4x + 4 \( -\,2^{38}\cdot 3\cdot 1061\cdot 24469\cdot 188414113\cdot 393131311\cdot 4977192294056925650789352450614791 \) $S_{38}$ (as 38T76) n/a
38.2.76837469450307682292059279224725537680200512645417292029451367237025792.1 x38 - 4x - 4 \( 2^{38}\cdot 727\cdot 5261563\cdot 73077559047116249833260249644378329868669917729193 \) $S_{38}$ (as 38T76) n/a
38.0.144970818688148423270805728938735241101988898053513592814114008664637440.1 x38 - 2x + 2 \( -\,2^{38}\cdot 5\cdot 41\cdot 367\cdot 263591\cdot 73599203\cdot 4905513061473881\cdot 73660168063921443246200957 \) $S_{38}$ (as 38T76) n/a
38.0.147872192092293515240287560992226440858040277966341129166293547068332971.1 x38 - x + 2 \( -\,27991188787\cdot 5282812145548104521106046048555288208740138420986354414469033 \) $S_{38}$ (as 38T76) n/a
38.0.147872192092304070375243338775640519188126273799287256562376917267775488.1 x38 + 2 \( -\,2^{75}\cdot 19^{38} \) 38T9 Trivial (GRH)
38.2.147872192092304070375243338775640519188126273799287256562376917267775488.1 x38 - 2 \( 2^{75}\cdot 19^{38} \) 38T9 Trivial (GRH)
38.2.150773565496459717479680948612545797274263649545060920310639825870913536.1 x38 - 2x - 2 \( 2^{38}\cdot 3\cdot 182837011981924924814764318838019240834623693499526077249223 \) $S_{38}$ (as 38T76) n/a
38.2.284791482692749835536885264940522098762203880501401727087795734405517578125.1 x38 - 5 \( 5^{37}\cdot 19^{38} \) 38T9 n/a
38.2.14258422185282661194839449228784338024756499615792788929321629765271215858317.1 x38 - 3x - 1 \( 487\cdot 521\cdot 4519\cdot 26317\cdot 11892563\cdot 39732930972782132460495746364538247928675306727948539379 \) $S_{38}$ (as 38T76) n/a
38.0.470207346404490340384495199475209233402018357248959736621334835182883335380339.1 x38 - 3x + 3 \( -\,3^{37}\cdot 11\cdot 71\cdot 7880009\cdot 21435017\cdot 7915920170803969017816295491376945943528821 \) $S_{38}$ (as 38T76) n/a
38.0.484465765688399596347775742286389752461067517871253000661505347854829883490304.1 x38 - 2x + 3 \( -\,2^{39}\cdot 523\cdot 599\cdot 213961453\cdot 35576001825507809\cdot 369549036309479457672944372639639227 \) $S_{38}$ (as 38T76) n/a
38.2.484465768589773000503422846723999589366345604008628746435169096117738486628352.1 x38 - 3 \( 2^{38}\cdot 3^{37}\cdot 19^{38} \) 38T9 n/a
38.2.498724190775055660622350493972789945330672850768297756249003357052593637876365.1 x38 - 3x - 3 \( 3^{37}\cdot 5\cdot 221515441369465466460532848622822255590773911416105332587571 \) $S_{38}$ (as 38T76) n/a
38.2.948879803050989584620936728952856178707584223842026603837566232766082191458304.1 x38 - 4x - 3 \( 2^{38}\cdot 40980168689701\cdot 203965927976641\cdot 412990441418705007555356829064473217351 \) $S_{38}$ (as 38T76) n/a
38.2.31900937949806586390320337463114855419174100233410480755209811568901372071903232.1 x38 - 4x - 2 \( 2^{75}\cdot 3\cdot 23\cdot 277\cdot 1513583473\cdot 5473293451459721\cdot 5332978185985420820488513531 \) $S_{38}$ (as 38T76) n/a
38.2.797523448449420275573400295827384707928071467459009471281670776097780467262029824.1 x38 - 4x + 2 \( 2^{75}\cdot 7\cdot 47\cdot 64164954126569673234813332462561408162487876014661903017 \) $S_{38}$ (as 38T76) n/a
38.2.797523448597292467664628454400648052721651557394279621301842545291326968465195008.1 x38 - 4x + 1 \( 2^{38}\cdot 3\cdot 811\cdot 2302291\cdot 517966057255956009554954225246160624258380010402927414479869 \) $S_{38}$ (as 38T76) n/a
38.0.5080849832193481021043781792889688288464476220368709136423318533586081437892739072.1 x38 - 2x + 4 \( -\,2^{36}\cdot 3\cdot 7\cdot 269683\cdot 243410960929\cdot 53634411417457511001169668118600282980215765726407141 \) $S_{38}$ (as 38T76) n/a
38.2.5080849832194931707745859616441907093382928859411777824296205365460212892194308096.1 x38 - 2x - 4 \( 2^{36}\cdot 101\cdot 919\cdot 1949\cdot 3539\cdot 185240700233\cdot 17140715362231\cdot 36371555198831357772204065739472223 \) $S_{38}$ (as 38T76) n/a
38.2.20323399328776825457579293373798146541478224237891059917271993925488672030373536853.1 x38 - x - 4 \( 773\cdot 4813\cdot 6781\cdot 44087\cdot 282407\cdot 4622799406751\cdot 23120981570369\cdot 605354715250981541649232676485669447 \) $S_{38}$ (as 38T76) n/a
38.0.2501696311112367702213593384284049957523786814936027691413131289153060507631187229631.1 x38 - x37 + 3x36 - 11x35 + 44x34 + 732x33 - 116x32 + 2069x31 + 2818x30 - 12880x29 + 93246x28 - 145805x27 + 92780x26 + 2105124x25 - 3183002x24 - 3104601x23 + 12583923x22 + 9706311x21 + 21916307x20 - 49619666x19 + 22159929x18 - 196911474x17 + 1026982112x16 + 311788273x15 - 1106984612x14 - 334730951x13 - 1752540110x12 + 3801710744x11 + 7280378790x10 + 1308968234x9 - 6926602921x8 - 6856588968x7 + 18604485712x6 + 18058309277x5 + 9272912074x4 - 5214869030x3 - 1463327624x2 + 5326526527x + 2048986499 \( -\,191^{37} \) $C_{38}$ (as 38T1) n/a
38.2.3839935727511250084381873285947946387767292827812861625609590641933945885923046717821.1 x38 - 5x + 1 \( 3\cdot 4921063777787\cdot 260102009166133812584985142358770156526818265636216301398179309035254861 \) $S_{38}$ (as 38T76) n/a
38.2.3839935727511250084381875437771550347755256948671367337857148872908683546755175938429.1 x38 - 5x - 1 \( 163\cdot 315952440047\cdot 735114279983971219\cdot 101428447464121945448827044448280047869601556164829131 \) $S_{38}$ (as 38T76) n/a
38.2.9124758045063636213395680721976151947343770081895790497970374417491257190704345703125.1 x38 - 5x - 5 \( 5^{37}\cdot 131\cdot 181\cdot 2011\cdot 898776624172831\cdot 2926290836145496407027696425922931571 \) $S_{38}$ (as 38T76) n/a
38.0.19570721669515368233701461995069628680180704735885478465656063556584062934272849215488.1 x38 - 2x + 5 \( -\,2^{39}\cdot 13\cdot 35869\cdot 88799\cdot 604309\cdot 6594677\cdot 27890279\cdot 25456155281264080123\cdot 303856164543774260275357 \) $S_{38}$ (as 38T76) n/a
38.0.74442950950550225751797377774065870790571380960577885518266630242578685283660888671875.1 x38 - 5x + 5 \( -\,5^{37}\cdot 23\cdot 139\cdot 299699\cdot 9433691167\cdot 85263102703\cdot 14613295519063\cdot 90847825344374471 \) $S_{38}$ (as 38T76) n/a
38.0.78282886663803053650896592016997971909542299884492753240330990186165739065144848751987.1 x38 - 3x + 5 \( -\,313\cdot 1019481121\cdot 8471154741571\cdot 28960142293866467628247950531735628005572712542426606634900089 \) $S_{38}$ (as 38T76) n/a
38.0.78282886678061475836179252135925619158332655848820000000000000000000000000000000000000.1 x38 + 5 \( -\,2^{38}\cdot 5^{37}\cdot 19^{38} \) 38T9 n/a
38.2.78282886678061475836179252146480754114110439262898330085995832946127396083370199442517.1 x38 - x - 5 \( 3\cdot 4441\cdot 68315627\cdot 8533124051989\cdot 10079446546039780216505179050024688541395414940881977168831593 \) $S_{38}$ (as 38T76) n/a
38.2.78282886678061478737552656291572723595942492754098086137375745773663748262908603138048.1 x38 - 2x - 5 \( 2^{39}\cdot 3\cdot 17\cdot 929\cdot 26261\cdot 1587413\cdot 12103709\cdot 158015743\cdot 1243193510457304691\cdot 30321616657803787127474779 \) $S_{38}$ (as 38T76) n/a
38.38.2060216431308955044384280937712919845834134545017995801607919643876646151404578845017109.1 x38 - x37 - 111x36 + 252x35 + 5215x34 - 18518x33 - 127217x32 + 667591x31 + 1483161x30 - 13721975x29 + 465004x28 + 166721208x27 - 256518740x26 - 1121099509x25 + 3587854285x24 + 2545487107x23 - 24194172078x22 + 18477975516x21 + 81929300895x20 - 167013913064x19 - 73340427022x18 + 542830510766x17 - 389253844535x16 - 713755295161x15 + 1324741808499x14 - 116683382685x13 - 1503618080692x12 + 1234820609168x11 + 402888989840x10 - 1097103201368x9 + 414161581992x8 + 265775405099x7 - 274544542564x6 + 51663795877x5 + 34067812864x4 - 20708103251x3 + 4233902513x2 - 281738990x - 6131569 \( 229^{37} \) $C_{38}$ (as 38T1) n/a
38.0.15223168714879313546692095257379448420591016496978036941227483116202289492875331751113046747.1 x38 - x37 + 91x36 - 24x35 + 5113x34 - 166x33 + 173717x32 + 27194x31 + 4239797x30 + 1325317x29 + 74027272x28 + 40999344x27 + 983326589x26 + 743120555x25 + 10059741791x24 + 9563481092x23 + 81070213075x22 + 87547591746x21 + 511882174610x20 + 601337789804x19 + 2539884758984x18 + 3042827513863x17 + 9675050790560x16 + 11543123809355x15 + 28268796522511x14 + 31776668507252x13 + 60600608962241x12 + 63076854532617x11 + 95016529831875x10 + 85766481354393x9 + 98440678914956x8 + 74640315704381x7 + 67352150639088x6 + 40110464366364x5 + 23287561297245x4 + 7350839404496x3 + 1810153278801x2 + 182761486103x + 13841287201 \( -\,3^{19}\cdot 191^{36} \) $C_{38}$ (as 38T1) n/a
38.0.2233638411813024816853081773648251688534529753590642239923912316757382599022775822751448518259.1 x38 - 209x35 + 190x34 + 1292x33 + 11818x32 - 17860x31 - 124165x30 + 92378x29 - 315590x28 + 461434x27 + 19355661x26 + 42336256x25 - 170675214x24 - 2184021538x23 + 4055379323x22 + 20028771815x21 - 37281886089x20 - 119372774190x19 + 206222273796x18 + 638565435242x17 - 1510749792677x16 - 1246896758667x15 + 6615154002166x14 + 1497131351993x13 + 895955914113x12 - 6914578071407x11 + 51068057863185x10 + 80278712330599x9 - 10972845112675x8 + 78343381011053x7 + 257531197354487x6 + 248070995565179x5 + 172436840306532x4 + 97988777901672x3 + 65070800259551x2 + 24610290628033x + 5454582062023 \( -\,19^{73} \) $C_{38}$ (as 38T1) n/a
38.38.2907625224541948887418190194159474648332884150922805055774449275194637293139188364462591928677.1 x38 - x37 - 188x36 + 180x35 + 15133x34 - 12829x33 - 695929x32 + 470210x31 + 20560148x30 - 9452291x29 - 414286793x28 + 90520176x27 + 5875939616x26 + 191303612x25 - 59496127537x24 - 16762796308x23 + 430644226744x22 + 224673611403x21 - 2206305371572x20 - 1655031822292x19 + 7828656065108x18 + 7607383848877x17 - 18551523651529x16 - 22355418258850x15 + 27686404325779x14 + 41724858463028x13 - 23225313872578x12 - 48637857116067x11 + 6837701957301x10 + 34223650023543x9 + 4693738691921x8 - 13444562674843x7 - 4790142874347x6 + 2352031466145x5 + 1507820068977x4 + 14043380009x3 - 154333274880x2 - 38062864399x - 2836879451 \( 3^{19}\cdot 191^{37} \) $C_{38}$ (as 38T1) n/a
38.0.3600319611560698860610362435063272860144872381060102455880973038531255093138465367428016635904.1 x38 + 181x36 + 14302x34 + 655785x32 + 19564842x30 + 403491764x28 + 5961216274x26 + 64460499272x24 + 516273473421x22 + 3076728313208x20 + 13620343868498x18 + 44444158242663x16 + 105381413708670x14 + 177560394917737x12 + 205585970435602x10 + 155336297697903x8 + 70268784621098x6 + 16089414412134x4 + 1207108975793x2 + 13841287201 \( -\,2^{38}\cdot 191^{36} \) $C_{38}$ (as 38T1) n/a
38.0.10456376296029042882633731329285387968875960938724861754483238620568507960573755104483627713707.1 x38 - x37 + 109x36 - 318x35 + 7607x34 - 26082x33 + 346271x32 - 1277601x31 + 11625429x30 - 40847577x29 + 278354747x28 - 890102893x27 + 4876149460x26 - 13377962627x25 + 59213347219x24 - 129738898417x23 + 497734200105x22 - 864588650146x21 + 3071362959747x20 - 3938571660134x19 + 13635086341776x18 - 11900678948488x17 + 45427254629183x16 - 23117165748554x15 + 104447793269632x14 - 20670309199584x13 + 172563580620384x12 + 14666610274324x11 + 167592119930922x10 + 69948796872392x9 + 125341715722354x8 + 63681900889938x7 + 64136735752211x6 + 36520042111943x5 + 22298249070088x4 + 8329262399475x3 + 2645555104756x2 + 468857415513x + 63175314409 \( -\,3^{19}\cdot 229^{36} \) $C_{38}$ (as 38T1) n/a
38.38.249822358047761737585176935673663749247824265938007663448506628820714951323582836933135986328125.1 x38 - 17x37 - 64x36 + 2589x35 - 5411x34 - 156768x33 + 733103x32 + 4788192x31 - 35074270x30 - 69778288x29 + 937716801x28 - 3988006x27 - 15662818901x26 + 18940301798x25 + 169186329709x24 - 366424944806x23 - 1167394423359x22 + 3780063487716x21 + 4693995261962x20 - 24515638087910x19 - 6315614627194x18 + 103828189076722x17 - 36155927083660x16 - 285274970106320x15 + 223944436674986x14 + 486329219734937x13 - 571966582999537x12 - 458764738319995x11 + 781485719820911x10 + 160103399248715x9 - 557488639455834x8 + 53135732479684x7 + 180915511892981x6 - 38184876354047x5 - 25486623807243x4 + 6173666606950x3 + 1214949029058x2 - 273982926995x + 184740541 \( 5^{19}\cdot 191^{36} \) $C_{38}$ (as 38T1) n/a
38.38.687661045808093482376579225097085116287670624782479569073265850359469722789446885178751177457664.1 x38 - 191x36 + 15662x34 - 730575x32 + 21705622x30 - 436357836x28 + 6157331558x26 - 62411853712x24 + 460944322269x22 - 2499589479956x20 + 9974553348782x18 - 29202012585177x16 + 62167403988174x14 - 94680464008195x12 + 100459885220950x10 - 71207905317537x8 + 31469275400290x6 - 7629511512714x4 + 744125807285x2 - 1101076991 \( 2^{38}\cdot 191^{37} \) $C_{38}$ (as 38T1) n/a
38.0.2394510171790650820123124474406353844872595054967993341776661644110188322971389918926750746438903.1 x38 - x37 + 118x36 - 435x35 + 6131x34 - 35235x33 + 222008x32 - 1286466x31 + 5995377x30 - 26936649x29 + 103513172x28 - 328397860x27 + 831795745x26 - 841346468x25 - 6703672958x24 + 58117415411x23 - 303731983764x22 + 1218275129036x21 - 3767355799065x20 + 7961894667643x19 - 2218796696910x18 - 81504663492211x17 + 502603614584717x16 - 2027971305796085x15 + 6509260330141933x14 - 17551631941921428x13 + 40524896388301467x12 - 80503012777500047x11 + 136388077021556601x10 - 193370722349898757x9 + 226309207994588218x8 - 220960831577107827x7 + 187038155057537519x6 - 141423416677434751x5 + 93202974532409581x4 - 51592635735804780x3 + 25439606449082092x2 - 11768916674310345x + 3447647463127489 \( -\,3^{19}\cdot 229^{37} \) $C_{38}$ (as 38T1) n/a
38.0.2472960613492762938009352687218362626942035203162587025151809700624254848124906369677396881178624.1 x38 + 217x36 + 20630x34 + 1139565x32 + 40850264x30 + 1004488522x28 + 17454519530x26 + 217550145613x24 + 1954462763213x22 + 12621446315235x20 + 58044125409037x18 + 187171442808726x16 + 413962321806804x14 + 609555286857416x12 + 575420256350720x10 + 333058518278260x8 + 111675903836641x6 + 20190511272319x4 + 1811471395871x2 + 63175314409 \( -\,2^{38}\cdot 229^{36} \) $C_{38}$ (as 38T1) n/a
38.0.10517653274833793910788391650485470831673313848992580618621786800117331392788597759645606697493139.1 x38 - x37 + 6x36 - 46x35 - 866x34 - 2262x33 - 8218x32 - 21902x31 + 431634x30 + 845654x29 + 12392062x28 + 22625646x27 + 131347110x26 + 99749222x25 + 35665294x24 - 866315187x23 - 258426421x22 + 17785842992x21 + 90256146871x20 + 153552360949x19 + 435041961961x18 - 1392669637447x17 + 1076840441256x16 - 9935143209215x15 + 31070017846749x14 - 17675958023404x13 + 138250934902501x12 - 327233950365006x11 + 433153745352823x10 - 1944991946784557x9 + 5889532748622531x8 - 11577094600459131x7 + 25495193933767723x6 - 50712315827213047x5 + 74651226530405679x4 - 82308207923451862x3 + 77528185035084423x2 - 59368882440546583x + 25758699005655811 \( -\,419^{37} \) $C_{38}$ (as 38T1) n/a
38.0.47716070387122491878768794713669776106334434794159463718664766104756555702804321854228973388671875.1 x38 - x37 + 194x36 - 202x35 + 16279x34 - 7863x33 + 772861x32 + 402596x31 + 23045822x30 + 40384193x29 + 479536671x28 + 1351816180x27 + 7928555878x26 + 25902608554x25 + 111456458601x24 + 341385389946x23 + 1297163210108x22 + 3493633650369x21 + 12095301942774x20 + 29754895552994x19 + 90602135732080x18 + 209292172135889x17 + 578704163180687x16 + 1150796400064466x15 + 3249066298571457x14 + 4892053641982278x13 + 14078439508345248x12 + 18448183569455711x11 + 46083907583218775x10 + 65495333977938485x9 + 111449247373051429x8 + 177739871270855783x7 + 253288222342260757x6 + 334042708854918147x5 + 456173375797126253x4 + 247500381632980217x3 + 331215018154218380x2 + 303420818935344453x + 79580728329881359 \( -\,5^{19}\cdot 191^{37} \) $C_{38}$ (as 38T1) n/a
38.38.261155635880173145190834143863916236459784105051247887526480662539321871437267060984748132072522857.1 x38 - x37 - 222x36 + 479x35 + 21047x34 - 66053x33 - 1110228x32 + 4495506x31 + 35823405x30 - 180946047x29 - 731415663x28 + 4712734359x27 + 9238434306x26 - 83665939703x25 - 59973164681x24 + 1044644450973x23 - 101098208429x22 - 9336414182461x21 + 6288159462034x20 + 60150648390199x19 - 67252981484387x18 - 278611442416743x17 + 417500804951451x16 + 915079337067075x15 - 1716002791423036x14 - 2065408719688167x13 + 4825202788269126x12 + 2982003177766905x11 - 9269437748788275x10 - 2187058821094830x9 + 11855288436035595x8 - 411608485430453x7 - 9515695267587717x6 + 2357948299236310x5 + 4196479083397002x4 - 1892165812751211x3 - 650631784472963x2 + 526610168112801x - 83497743723127 \( 457^{37} \) $C_{38}$ (as 38T1) n/a
38.0.566307980489842712804141765373005041569726061524232428759764421442954360220603558656123885789904896.1 x38 + 229x36 + 22442x34 + 1242325x32 + 43174744x30 + 989928070x28 + 15310092242x26 + 160462320009x24 + 1129846290713x22 + 5241767939799x20 + 15619544332617x18 + 29338707057674x16 + 34962128493052x14 + 26729901012072x12 + 13161379227544x10 + 4139430890096x8 + 811133080337x6 + 94183964323x4 + 5864318791x2 + 149876149 \( -\,2^{38}\cdot 229^{37} \) $C_{38}$ (as 38T1) n/a
38.0.136635360908492439649635218195335734184282612187547808802428015665989693822130747061222659537193769787.1 x38 + 171x36 - 266x35 + 17765x34 - 38323x33 + 1208419x32 - 3128616x31 + 60877083x30 - 164538138x29 + 2281935169x28 - 6108816122x27 + 65770773122x26 - 164067939585x25 + 1434043198618x24 - 3182597959136x23 + 23807715304970x22 - 44488778447299x21 + 291967423046375x20 - 424722852053838x19 + 2667130160996125x18 - 2974990157993691x17 + 18341053997864450x16 - 14685757775285777x15 + 92760878311304464x14 - 59049250104163667x13 + 342353164732402796x12 - 172475502215832115x11 + 890393108976853995x10 - 452012764582067042x9 + 1563583757111096932x8 - 707974172043966504x7 + 1816769368682524829x6 - 831929210861393479x5 + 1134167336866808190x4 - 228910989279510535x3 + 271437005032832706x2 - 30519054068376079x + 49228485006254761 \( -\,3^{19}\cdot 19^{72} \) $C_{38}$ (as 38T1) n/a

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