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Label Polynomial Discriminant Galois group Class group
45.45.977...089.1 x45 - x44 - 72x43 + 67x42 + 2321x41 - 2007x40 - 44393x39 + 35655x38 + 562984x37 - 420187x36 - 5012298x35 + 3480849x34 + 32367724x33 - 20955723x32 - 154542085x31 + 93497512x30 + 551503498x29 - 312562651x28 - 1478859633x27 + 786888918x26 + 2984367290x25 - 1493106677x24 - 4527360022x23 + 2130398676x22 + 5146818792x21 - 2274599139x20 - 4361796744x19 + 1804001386x18 + 2733500368x17 - 1051995625x16 - 1251105602x15 + 444673277x14 + 410259354x13 - 133494819x12 - 93584992x11 + 27616610x10 + 14189768x9 - 3755862x8 - 1331682x7 + 310282x6 + 69020x5 - 13468x4 - 1660x3 + 232x2 + 16x - 1 \( 7^{30}\cdot 31^{42} \) $C_3\times C_{15}$ (as 45T2) trivial (GRH)
45.45.183...361.1 x45 - 87x43 - 4x42 + 3402x41 + 300x40 - 79106x39 - 10008x38 + 1219668x37 + 196264x36 - 13165542x35 - 2519472x34 + 102436164x33 + 22316760x32 - 583045167x31 - 140145264x30 + 2440735434x29 + 631757436x28 - 7504722910x27 - 2050106328x26 + 16845457116x25 + 4771066968x24 - 27354225744x23 - 7899876240x22 + 31819110888x21 + 9218870784x20 - 26289431304x19 - 7517163552x18 + 15324352272x17 + 4245866400x16 - 6258116631x15 - 1643669037x14 + 1770836592x13 + 429144192x12 - 340508538x11 - 73586928x10 + 43022076x9 + 7934841x8 - 3375522x7 - 502012x6 + 149688x5 + 16758x4 - 3200x3 - 252x2 + 24x + 1 \( 3^{60}\cdot 31^{42} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.295...689.1 x45 - 3x44 - 108x43 + 296x42 + 5217x41 - 13005x40 - 149828x39 + 337863x38 + 2868057x37 - 5809689x36 - 38881407x35 + 70098207x34 + 387120467x33 - 613625013x32 - 2896408122x31 + 3972622452x30 + 16519787829x29 - 19205853294x28 - 72406643558x27 + 69489283683x26 + 244599321027x25 - 187254237300x24 - 635787323022x23 + 371102281773x22 + 1263897395760x21 - 528600088722x20 - 1901669780781x19 + 520023114157x18 + 2134290033054x17 - 327330093672x16 - 1754567507744x15 + 107410900356x14 + 1034842778925x13 + 1036802542x12 - 428135520330x11 - 14111627571x10 + 121049080943x9 + 4346148948x8 - 22551409551x7 - 290753084x6 + 2597605155x5 - 77625633x4 - 161647682x3 + 13050165x2 + 3741168x - 437977 \( 3^{60}\cdot 7^{30}\cdot 11^{36} \) $C_3\times C_{15}$ (as 45T2) trivial (GRH)
45.45.113...889.1 x45 - 12x44 - 38x43 + 936x42 - 488x41 - 32994x40 + 61155x39 + 695151x38 - 1826452x37 - 9745559x36 + 31398650x35 + 95576968x34 - 363031278x33 - 668271620x32 + 3006554151x31 + 3299628259x30 - 18405469866x29 - 10819187452x28 + 84606290574x27 + 17798672756x26 - 293624042239x25 + 25779977473x24 + 766879229695x23 - 259704306954x22 - 1488735953755x21 + 843265985246x20 + 2094958274346x19 - 1672596038928x18 - 2036992655261x17 + 2211683013511x16 + 1229593352332x15 - 1960884055901x14 - 305227614428x13 + 1128154934100x12 - 126915280282x11 - 391023252143x10 + 124192084723x9 + 69369604379x8 - 37452923715x7 - 3334757683x6 + 4610823573x5 - 413774775x4 - 188088413x3 + 35065204x2 - 872335x + 619 \( 13^{30}\cdot 31^{42} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.217...129.1 x45 - 12x44 - 50x43 + 1120x42 - 626x41 - 44264x40 + 106520x39 + 966733x38 - 3644562x37 - 12564205x36 + 68449875x35 + 92270622x34 - 830216501x33 - 202049055x32 + 6933616229x31 - 3181542881x30 - 41084005259x29 + 40234212427x28 + 174510130968x27 - 250382990469x26 - 527354195438x25 + 1015613064703x24 + 1094857977723x23 - 2871848912941x22 - 1403630755463x21 + 5763542313829x20 + 629825101852x19 - 8167242308412x18 + 1257688359124x17 + 7983130477206x16 - 2778691581109x15 - 5144196139934x14 + 2589633668016x13 + 2011525458240x12 - 1316532612469x11 - 396963769511x10 + 358975449036x9 + 14178066293x8 - 45168898819x7 + 5258463166x6 + 1537215457x5 - 288043322x4 - 5291206x3 + 2457345x2 - 9309x - 6089 \( 7^{30}\cdot 61^{42} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.999...561.1 x45 - 12x44 - 68x43 + 1390x42 - 278x41 - 68270x40 + 176199x39 + 1808389x38 - 8154574x37 - 26005805x36 + 196321268x35 + 127187382x34 - 2913805970x33 + 2272631340x32 + 27669670927x31 - 52510157887x30 - 162002621792x29 + 526806359978x28 + 468745083598x27 - 3175101889498x26 + 532391340063x25 + 12135569776697x24 - 10651958891479x23 - 28871893561060x22 + 45196495080913x21 + 38272655903792x20 - 105664143365844x19 - 13349385343870x18 + 153132315545987x17 - 41028745873427x16 - 141811047613612x15 + 76543731297893x14 + 83515595010770x13 - 65499266094722x12 - 29808531214812x11 + 32918818373161x10 + 5404646072895x9 - 10084991417837x8 - 16286468525x7 + 1821205338619x6 - 180698614131x5 - 173451418339x4 + 28592722199x3 + 6396948952x2 - 1303357845x - 3078919 \( 19^{30}\cdot 31^{42} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.408...321.1 x45 - 3x44 - 126x43 + 350x42 + 7095x41 - 18207x40 - 237254x39 + 560949x38 + 5280957x37 - 11465163x36 - 83127609x35 + 164960568x34 + 959694733x33 - 1729668720x32 - 8316855543x31 + 13495839126x30 + 54911329452x29 - 79318322604x28 - 278624618803x27 + 353264598507x26 + 1090386630918x25 - 1193881051406x24 - 3286918329246x23 + 3054422504946x22 + 7584376524784x21 - 5885779838802x20 - 13239515051214x19 + 8489225140885x18 + 17170281215082x17 - 9118144480932x16 - 16115327765898x15 + 7281918623109x14 + 10535410010724x13 - 4323241543716x12 - 4518883017183x11 + 1877328461526x10 + 1138556965481x9 - 554295751305x8 - 124509763362x7 + 91825606123x6 - 3656082528x5 - 5240896776x4 + 961503906x3 - 1541688x2 - 11847522x + 756289 \( 3^{60}\cdot 61^{42} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.202...625.1 x45 - 165x43 - 25x42 + 12060x41 + 3486x40 - 519330x39 - 214140x38 + 14776560x37 + 7718745x36 - 295077669x35 - 182852610x34 + 4284179615x33 + 3016157820x32 - 46197393465x31 - 35772719505x30 + 374607222195x29 + 310484223975x28 - 2298730688540x27 - 1988244775980x26 + 10695933805596x25 + 9407317026635x24 - 37696094037390x23 - 32764647222885x22 + 100289481110340x21 + 83332538318277x20 - 200279250507195x19 - 152889355168310x18 + 297466429398705x17 + 198745289480940x16 - 323624520119411x15 - 178210655500665x14 + 251547979741875x13 + 105785393431525x12 - 134218212107550x11 - 38927292179565x10 + 46104688292390x9 + 7956837983055x8 - 9173261413650x7 - 765305596255x6 + 891053703312x5 + 40709257785x4 - 38148076985x3 - 1973427960x2 + 606052050x + 47691757 \( 3^{60}\cdot 5^{72}\cdot 7^{30} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.252...929.1 x45 - 12x44 - 80x43 + 1424x42 + 1516x41 - 74554x40 + 63158x39 + 2282501x38 - 4255902x37 - 45636421x36 + 116693559x35 + 630121996x34 - 1971613347x33 - 6193698077x32 + 22855343401x31 + 44007670585x30 - 190617019593x29 - 226920195907x28 + 1172746429282x27 + 842990049201x26 - 5394671280584x25 - 2206384597765x24 + 18666651459717x23 + 3871477687999x22 - 48596558981735x21 - 4036750693451x20 + 94693820108958x19 + 1546861746446x18 - 136570614884744x17 + 956863921562x16 + 143064103358001x15 + 102341290612x14 - 105649963477592x13 - 2816833651750x12 + 52484763220205x11 + 2919265367283x10 - 16311452643376x9 - 1104335997267x8 + 2857645920655x7 + 105919440856x6 - 255094574859x5 + 8466426668x4 + 8654209646x3 - 1026667213x2 + 14388119x + 1507921 \( 13^{30}\cdot 61^{42} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.235...625.1 x45 - 15x44 - 90x43 + 2245x42 + 840x41 - 149682x40 + 233625x39 + 5893830x38 - 15309120x37 - 153159405x36 + 505833687x35 + 2780167860x34 - 10777640365x33 - 36390969195x32 + 160894854450x31 + 349558305696x30 - 1751940770010x29 - 2483116182570x28 + 14226276458010x27 + 13037929556940x26 - 87229174471284x25 - 50137706272620x24 + 406336593221610x23 + 138267603359730x22 - 1439822630956295x21 - 262195938148443x20 + 3868718864967360x19 + 311910060390275x18 - 7821266721741750x17 - 175081417856730x16 + 11738415157749574x15 - 32411856380685x14 - 12806776910595090x13 + 44301971232950x12 + 9836514943009755x11 + 117791800035840x10 - 5063789878500180x9 - 176503490451285x8 + 1618208036238660x7 + 90536277582715x6 - 283553373081756x5 - 18640864878495x4 + 21751317924475x3 + 974579665770x2 - 434206226325x + 15265738099 \( 3^{60}\cdot 5^{72}\cdot 13^{30} \) $C_3\times C_{15}$ (as 45T2) n/a
45.45.206...625.1 x45 - 15x44 - 120x43 + 2785x42 + 2040x41 - 222342x40 + 420425x39 + 10024590x38 - 35069730x37 - 280556895x36 + 1389459441x35 + 4980489270x34 - 34327919505x33 - 52485204525x32 + 576080544270x31 + 196092367854x30 - 6820772763030x29 + 3051952728270x28 + 57922300812880x27 - 59937846525180x26 - 353495076875202x25 + 542694665981220x24 + 1531071286376460x23 - 3131712122030760x22 - 4545064586341055x21 + 12339167509476885x20 + 8461213880546430x19 - 33709107574234355x18 - 6968642817313350x17 + 63373889569191960x16 - 7076452922900098x15 - 80218608988132905x14 + 26470314281644410x13 + 66243722166245240x12 - 32060240741785995x11 - 34356066621763764x10 + 20781515138515650x9 + 10477766738441505x8 - 7675031336820660x7 - 1594722107742745x6 + 1559444254090284x5 + 49643486026125x4 - 150881459933485x3 + 10931860799430x2 + 4297070637735x - 401780151251 \( 3^{60}\cdot 5^{72}\cdot 19^{30} \) $C_3\times C_{15}$ (as 45T2) n/a
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