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Results (displaying all 17 matches)

Label Polynomial Discriminant Galois group Class group
17.17.160470643909878751793805444097921.1 x17 - x16 - 48x15 + 105x14 + 763x13 - 2579x12 - 3653x11 + 23311x10 - 11031x9 - 74838x8 + 107759x7 + 50288x6 - 198615x5 + 102976x4 + 58507x3 - 75722x2 + 25763x - 2837 \( 103^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.2349760091653551409013119601402609.1 x17 - 4x16 - 11x15 + 53x14 + 44x13 - 271x12 - 81x11 + 676x10 + 78x9 - 866x8 - 56x7 + 563x6 + 36x5 - 176x4 - 12x3 + 23x2 + x - 1 \( 19501\cdot 163667513\cdot 736214146077100976893 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.17.15400296222263289476715621650663041.1 x17 - x16 - 64x15 + 43x14 + 1478x13 - 932x12 - 16008x11 + 12183x10 + 86347x9 - 84507x8 - 213223x7 + 271237x6 + 152800x5 - 314540x4 + 100605x3 + 20132x2 - 13981x + 1681 \( 137^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.597436338855434422471226103296950272.1 x17 - 51x15 + 1071x13 - 11934x11 + 75735x9 - 272646x7 + 520506x5 - 446148x3 + 111537x - 22482 \( 2^{24}\cdot 3^{16}\cdot 17^{17} \) $F_{17}$ (as 17T5) Trivial (GRH)
17.17.8272402618863367641770000000000000000.1 x17 - 85x15 + 2975x13 - 55250x11 + 584375x9 - 3506250x7 + 11156250x5 - 15937500x3 + 6640625x - 1737500 \( 2^{16}\cdot 5^{16}\cdot 17^{17} \) $F_{17}$ (as 17T5) Trivial (GRH)
17.17.113335617496346216833223278514633468161.1 x17 - x16 - 112x15 + 47x14 + 3976x13 - 4314x12 - 64388x11 + 136247x10 + 422013x9 - 1631073x8 + 411840x7 + 5840196x6 - 11894369x5 + 10635750x4 - 4739804x3 + 938485x2 - 54850x + 619 \( 239^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.2367911594760467245844106297320951247361.1 x17 - 136x15 - 85x14 + 6154x13 + 6545x12 - 119680x11 - 168555x10 + 998835x9 + 1749300x8 - 2783546x7 - 6581040x6 - 678725x5 + 3813882x4 + 770593x3 - 616267x2 - 82620x + 577 \( 17^{32} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.6226070121392010397563990173530787496001.1 x17 - x16 - 144x15 + 241x14 + 6894x13 - 14938x12 - 127923x11 + 323969x10 + 847982x9 - 2194186x8 - 2617873x7 + 6091397x6 + 3745755x5 - 7069429x4 - 1600190x3 + 3100257x2 - 220118x - 208777 \( 307^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.613158747081871736694796283376344205805441.1 x17 - x16 - 192x15 + 273x14 + 14752x13 - 28028x12 - 571107x11 + 1411675x10 + 11275657x9 - 36814399x8 - 91832077x7 + 461179352x6 - 109192148x5 - 1929139488x4 + 3679722325x3 - 2767754010x2 + 828153361x - 45886883 \( 409^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.2200187128095499475530336818113367454680001.1 x17 - x16 - 208x15 - 17x14 + 15287x13 + 13881x12 - 487578x11 - 703261x10 + 6754359x9 + 10540902x8 - 41136753x7 - 57683825x6 + 92010954x5 + 95287840x4 - 17501435x3 - 25026156x2 - 563260x + 1246103 \( 443^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.397527879693854754943959770157821268619247041.1 x17 - x16 - 288x15 + 265x14 + 26034x13 - 40228x12 - 875968x11 + 2022008x10 + 8464009x9 - 27681440x8 - 8855367x7 + 101412811x6 - 87313302x5 - 38624139x4 + 67164168x3 - 7149746x2 - 7878215x - 664471 \( 613^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.942906198449660107953222334097149309547713921.1 x17 - x16 - 304x15 + 1117x14 + 25631x13 - 126439x12 - 773932x11 + 4360454x10 + 10731832x9 - 64676368x8 - 79260104x7 + 441919082x6 + 345306489x5 - 1259087517x4 - 718017711x3 + 1025767171x2 + 183044979x - 202031659 \( 647^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.258850007664814362506653464185428842369437873281.1 x17 - x16 - 432x15 + 1911x14 + 56071x13 - 377127x12 - 2275999x11 + 22947072x10 - 5751373x9 - 395586237x8 + 1094097337x7 - 39485017x6 - 2920148551x5 + 2341974035x4 + 1284864535x3 - 1464500037x2 - 140787928x + 238840843 \( 919^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.462899178676311160288470191817767102492054133121.1 x17 - x16 - 448x15 + 1309x14 + 75494x13 - 374314x12 - 5597667x11 + 41830550x10 + 136426018x9 - 1919481097x8 + 2548312782x7 + 27117309376x6 - 105628969954x5 + 34101907629x4 + 457076113374x3 - 817186035962x2 + 323264486326x + 117028501127 \( 953^{16} \) $C_{17}$ (as 17T1) Trivial (GRH)
17.17.8972555039016074378226050552414591426720707963201.1 x17 - 4x16 - 476x15 + 3026x14 + 82996x13 - 736812x12 - 6121180x11 + 80531352x10 + 108448584x9 - 4267795762x8 + 9723361580x7 + 95353221324x6 - 524744382701x5 - 7660737412x4 + 6800548404356x3 - 21491689501032x2 + 27480501953536x - 12878683864992 \( 17^{12}\cdot 137^{16} \) $C_{17}:C_{4}$ (as 17T3) $[17]$ (GRH)
17.17.54471546860208560987402602575661525149433755592659973376605441.1 x17 - 3502x15 - 21012x14 + 3586048x13 + 27140500x12 - 1455974010x11 - 13391942168x10 + 247158969538x9 + 2699830692822x8 - 15367054046543x7 - 210262575924428x6 + 207808365630713x5 + 5600534069106679x4 + 891648638079425x3 - 50160692092741008x2 - 11309428987726617x + 145001801906376687 \( 17^{24}\cdot 103^{16} \) $D_{17}$ (as 17T2) $[17]$ (GRH)
17.17.13202363705223218603863184487755024630582383374680032800435939704158233027841788543229812635151072074455438626669432759450899735549243294921243306854586939663055181335880903211540683502950935087551803286773305471032026037990460071805978402769130092019752634101527352693814943791414905342572852579428180829030727661698750961477408713596845181881409326113271279701186934711912924535979375368089471422837282452421683506180048924876364820225210846226099372878635447796099920054239935070472348193791925328690838569369798938742618818040823435236370214291386195573062935332270993039421387687573397220106241394348907347636983408333263308765625.1 x17 - x16 - 209366104215680788999237026547641097698x15 - 1366742178334204175438997589171142015450323754334864369224x14 + 1370561167639445232641588842226596440326814811500377916577951156785205603616x13 + 34209858818572450923271706624028583128577132326587729764418829056155931883100572576543824614528x12 + 71060716298265833814190789484351947045094218086339373134017972529231516080624594299417621901900363029200839303680x11 - 181236556545551870194910603673122664616069745538191536145261133196422743167811347834952322646822461893016382882736111475051779835904x10 - 817453198936905169400742982687958866786256736846211649117725561020133238029973092638151864726931584027480499685581465329622501783309527162528308953088x9 - 406211134121143976571685932629427590329091770245795527373565243496924271345193026030870366206101859233901646299537618309720564689896228499629423779408143210096201302016x8 + 2063531180788517939004478109589742385478341534165997591626727610318370449381138162515361508202768867158479874086973104044545239342671435605273745820464492333093544875731405829610829512704x7 + 2896803440617034044082414054987092761425750561697541270975110048759818875866509904308337299406705399859448559468574920740735545763509144483628181748157772929773317331584643514549841613609047826134345449472x6 - 375728305046657587737437465141770466545137888085020499189518494157931590235776407255542703786899002623272850956760756590809799855663980937838753932085061186815235816159448759232674149349127567492283556692575228386248491008x5 - 2028919226122184282547719212404001304737799778058571160592238734166677967718184072440967382731107200224913576726869639337803258702187932484385556935885816415960345072227073330391030176232986366904452017071983642624332203614381743366125649920x4 - 60950714931147330950883801576283829013554502185033270196914465261994309923209703228786783036281560981312017861209153204720278213626389686597733457144020261637634080923052038123091922379051430144899539652593795568496537218812938586685114185884150715956330496x3 + 473928342892602293775643808769935031032066044095325682751754761239780409526186786886030926973533412678310396818663456261230461382663715105662885481585059970820106413547922797015360830616935208666603580522235685986237133614930548698028016260214317835178831217789563984521723904x2 - 65099622270587978065879038307806761197287013260747074255596854482937931422598383015653598654694045742457209039856196858466593297405172185778252691948608216506703929894692225332579595112013433301461138197138219492068735859226815044137679851709559000898305443997308036303693844239426410642407424x + 2014755577973807885553442175684655281473176522202931711918446863791222851942996378810544272763907161070021710559899467068574306440431996593428915637864458100949970854924532577927598683969894319931563502807289188851993089743098110146672995634255495997519516339298306955127636879610909991217001038430549642838016 \( 5^{6}\cdot 11^{4}\cdot 7596795978638745309377894608330080161099683005881415889061359860967619588462415760814465048343978782699623713340591203338379520292163715364016214101729599276737580457529860033268784695058881563931503800621993859955086365135567084414259503312082362048547343103953451218874990807007672764161961256815656908835269889^{2} \) $A_{17}$ (as 17T9) n/a


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