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Label Polynomial Discriminant Galois group Class group
37.1.104...381.1 x37 - x - 1 \( 983\cdot 10629448216535164688983333275934258954615695043479491507 \) $S_{37}$ (as 37T11) trivial (GRH)
37.1.106...653.1 x37 + x - 1 \( 19\cdot 11323755688122007063\cdot 49553590598385949034316572009816214049 \) $S_{37}$ (as 37T11) trivial (GRH)
37.1.146...709.1 x37 + 2x - 1 \( 13\cdot 79\cdot 3203\cdot 230203\cdot 34944191\cdot 52002217\cdot 4124383231\cdot 2576354638936903184957678084959 \) $S_{37}$ (as 37T11) trivial (GRH)
37.1.696...128.1 x37 - 4x - 4 \( 2^{36}\cdot 233\cdot 373\cdot 78191\cdot 71872279\cdot 16291354255739\cdot 1273067852382060949050712307 \) $S_{37}$ (as 37T11) n/a
37.1.710...320.1 x37 - 2x - 2 \( 2^{36}\cdot 5\cdot 7\cdot 151\cdot 9239\cdot 119446257446842253309\cdot 1773279344027073506762745149507 \) $S_{37}$ (as 37T11) n/a
37.1.725...376.1 x37 - x - 2 \( 2^{36}\cdot 255111423183900271\cdot 31886261543528230373\cdot 1297568460899930754527 \) $S_{37}$ (as 37T11) n/a
37.1.725...736.1 x37 - x - 4 \( 2^{38}\cdot 40158589\cdot 859997730921167\cdot 76406102828442561567149509932891263 \) $S_{37}$ (as 37T11) n/a
37.1.725...512.1 x37 - 2 \( 2^{36}\cdot 37^{37} \) $F_{37}$ (as 37T9) n/a
37.1.739...704.1 x37 + 2x - 2 \( 2^{36}\cdot 11\cdot 13\cdot 29\cdot 8111\cdot 320127488203456295874894895225917443149549690432217 \) $S_{37}$ (as 37T11) trivial (GRH)
37.1.754...896.1 x37 + 4x - 4 \( 2^{36}\cdot 41\cdot 11851181\cdot 1770736411\cdot 12762330988939184848269187144911016406131 \) $S_{37}$ (as 37T11) n/a
37.3.479...851.1 x37 - 3x - 1 \( -\,11\cdot 103\cdot 13781\cdot 868727\cdot 1508693\cdot 35096465749296997\cdot 66698832184480824114267204189107205461 \) $S_{37}$ (as 37T11) n/a
37.1.479...885.1 x37 + 3x - 1 \( 5\cdot 17\cdot 23\cdot 503\cdot 8237\cdot 17707\cdot 6366766785751\cdot 52460051211611194792761741742183151785898813561 \) $S_{37}$ (as 37T11) n/a
37.1.652...077.1 x37 + 3x - 3 \( 3^{36}\cdot 211\cdot 6139531\cdot 8271665508919\cdot 6321124050660239\cdot 6421792279973985077 \) $S_{37}$ (as 37T11) n/a
37.1.153...189.1 x37 - 3x - 3 \( 3^{36}\cdot 9598397\cdot 1066425245695362865242518064082832140086192779531897 \) $S_{37}$ (as 37T11) n/a
37.1.158...365.1 x37 - 2x - 3 \( 3^{36}\cdot 5\cdot 7\cdot 1493\cdot 137771\cdot 867792304013\cdot 1689516079471188538301539488375841381 \) $S_{37}$ (as 37T11) n/a
37.1.158...421.1 x37 - x - 3 \( 3^{36}\cdot 10555134955777783413369528211010741100746051776360630281301 \) $S_{37}$ (as 37T11) n/a
37.1.158...557.1 x37 - 3 \( 3^{36}\cdot 37^{37} \) $F_{37}$ (as 37T9) n/a
37.1.158...693.1 x37 + x - 3 \( 3^{36}\cdot 19\cdot 349\cdot 4501649\cdot 1182640248703\cdot 298992626266134903114276977887761869 \) $S_{37}$ (as 37T11) n/a
37.37.171...601.1 x37 - x36 - 72x35 + 67x34 + 2278x33 - 1964x32 - 41849x31 + 33262x30 + 497142x29 - 362207x28 - 4027127x27 + 2672215x26 + 22871279x25 - 13719683x24 - 92273266x23 + 49606380x22 + 265291071x21 - 126402144x20 - 540999671x19 + 224635365x18 + 773506030x17 - 271832880x16 - 761221384x15 + 214848879x14 + 502240682x13 - 103923082x12 - 213804070x11 + 27920639x10 + 55105551x9 - 3603129x8 - 7708785x7 + 235974x6 + 497852x5 - 22640x4 - 12819x3 + 1020x2 + 28x - 1 \( 149^{36} \) $C_{37}$ (as 37T1) trivial (GRH)
37.3.200...112.1 x37 - 4x - 2 \( -\,2^{36}\cdot 1181\cdot 156768103\cdot 3595021207\cdot 43936029316369609267530878765450907957409376167 \) $S_{37}$ (as 37T11) n/a
37.3.200...107.1 x37 - 4x - 1 \( -\,53\cdot 139\cdot 272784090122102222942634634990148406700978727237601926487597835998118772221 \) $S_{37}$ (as 37T11) n/a
37.1.200...136.1 x37 + 4x - 2 \( 2^{36}\cdot 249494962454898495919\cdot 117210921892231802991083559854148086237602430779 \) $S_{37}$ (as 37T11) n/a
37.1.201...181.1 x37 + 4x - 3 \( 3^{36}\cdot 839348831\cdot 15964094438173835184448798598426127689000924646813131 \) $S_{37}$ (as 37T11) n/a
37.1.124...160.1 x37 - 2x - 4 \( 2^{70}\cdot 5\cdot 7\cdot 47\cdot 6416495413844794610590562045489832191536616174274299017 \) $S_{37}$ (as 37T11) n/a
37.1.124...256.1 x37 + 2x - 4 \( 2^{70}\cdot 13\cdot 137\cdot 195791\cdot 10489284688357\cdot 5723750340436657\cdot 504174169295944373011 \) $S_{37}$ (as 37T11) n/a
37.1.498...464.1 x37 - 3x - 4 \( 2^{73}\cdot 9739\cdot 174331\cdot 36662321\cdot 289516438999\cdot 95795519149931\cdot 3057074418307037 \) $S_{37}$ (as 37T11) n/a
37.1.498...968.1 x37 + x - 4 \( 2^{73}\cdot 19\cdot 311\cdot 20831443951883\cdot 42874634453434399132146156864633660142157 \) $S_{37}$ (as 37T11) n/a
37.1.860...173.1 x37 + 5x - 3 \( 3^{34}\cdot 7\cdot 17\cdot 439\cdot 4064647\cdot 22665391718591\cdot 10715626350203244838440932001241748830381 \) $S_{37}$ (as 37T11) n/a
37.1.193...128.1 x37 + 5x - 2 \( 2^{34}\cdot 7\cdot 8599\cdot 1088665069\cdot 284461581404201\cdot 6042775319827757042577682747252314349278401 \) $S_{37}$ (as 37T11) n/a
37.3.774...443.1 x37 - 5x - 3 \( -\,3^{36}\cdot 43\cdot 1907\cdot 628920542887497981159697213468981036867441297942755778951483 \) $S_{37}$ (as 37T11) n/a
37.1.774...517.1 x37 + 5x - 1 \( 7\cdot 47\cdot 23527960918355024050600268022161542553882410207690230990373696435854356748326573 \) $S_{37}$ (as 37T11) n/a
37.1.779...832.1 x37 + 5x - 4 \( 2^{73}\cdot 7\cdot 37573\cdot 161999\cdot 10047643\cdot 4972224617011\cdot 387504669093621087013178459593 \) $S_{37}$ (as 37T11) n/a
37.1.145...125.1 x37 - 5x - 5 \( 5^{36}\cdot 563\cdot 175944697081\cdot 746724389353\cdot 135506897950212373247345664177143 \) $S_{37}$ (as 37T11) n/a
37.1.153...501.1 x37 - 4x - 5 \( 153595419500058073848198545529899006509355415341070933860109410036198707142370058501 \) $S_{37}$ (as 37T11) n/a
37.1.153...757.1 x37 - 3x - 5 \( 47\cdot 4458653\cdot 39030547\cdot 4191145897\cdot 2748399402101\cdot 46040166590110289\cdot 35410190689086361595487217777 \) $S_{37}$ (as 37T11) n/a
37.1.153...933.1 x37 - 2x - 5 \( 7\cdot 34591\cdot 96167\cdot 163386011\cdot 40372147503946792498117026681556583698165224878117054736922190257 \) $S_{37}$ (as 37T11) n/a
37.1.153...989.1 x37 - x - 5 \( 11\cdot 107\cdot 359\cdot 60013\cdot 22231407377\cdot 272458738133730168671247113586306799544259298022362102368018823 \) $S_{37}$ (as 37T11) n/a
37.1.153...125.1 x37 - 5 \( 5^{36}\cdot 37^{37} \) $F_{37}$ (as 37T9) n/a
37.1.161...125.1 x37 + 5x - 5 \( 5^{36}\cdot 7\cdot 17\cdot 39619\cdot 50081864423\cdot 2601293855703705209\cdot 18050801224775844479711 \) $S_{37}$ (as 37T11) n/a
37.37.345...561.1 x37 - x36 - 108x35 + 245x34 + 4913x33 - 17429x32 - 115073x31 + 605121x30 + 1258904x29 - 11895493x28 + 1401577x27 + 136786740x26 - 218698801x25 - 851925353x24 + 2810760540x23 + 1559768964x22 - 17408647490x21 + 14765496491x20 + 52555917850x19 - 112901823056x18 - 30825357400x17 + 320568348295x16 - 255996383256x15 - 343575615312x14 + 697695088122x13 - 135330997139x12 - 635742178755x11 + 559084397332x10 + 98854779029x9 - 379266961937x8 + 152281955055x7 + 65816775545x6 - 70480276872x5 + 12914339542x4 + 6483753572x3 - 3469705332x2 + 579396241x - 30247313 \( 223^{36} \) $C_{37}$ (as 37T1) trivial (GRH)
37.37.676...801.1 x37 - x36 - 288x35 + 203x34 + 35910x33 - 17336x32 - 2554843x31 + 842615x30 + 115283443x29 - 27504461x28 - 3475263507x27 + 687931612x26 + 71915662407x25 - 13974595438x24 - 1034496050617x23 + 221330910643x22 + 10365088714029x21 - 2534502436630x20 - 71813314605418x19 + 19740632343658x18 + 338381715805464x17 - 99305962871851x16 - 1055972317034939x15 + 302779333586209x14 + 2104618406390649x13 - 505910437546894x12 - 2560928454934750x11 + 376597618487442x10 + 1787314591059035x9 - 20429122626927x8 - 643936928000107x7 - 89391122404607x6 + 89662863870162x5 + 25891375086732x4 + 1113091773432x3 - 112807611860x2 - 8478121776x - 123515969 \( 593^{36} \) $C_{37}$ (as 37T1) n/a
37.37.813...681.1 x37 - 666x35 - 481x34 + 193399x33 + 256521x32 - 32436827x31 - 60004084x30 + 3503452596x29 + 8113398850x28 - 257000630926x27 - 704292185114x26 + 13150853376643x25 + 41268101524916x24 - 474337598223255x23 - 1672482254287228x22 + 12032466243732809x21 + 47286637172470867x20 - 211502629431882231x19 - 929675982328753625x18 + 2498958523266151636x17 + 12536142236443615902x16 - 18791897342800992970x15 - 113239929214497210129x14 + 80927529107744817385x13 + 663966210336111429023x12 - 146546651897009713442x11 - 2439258160361411529393x10 - 154326326264692800324x9 + 5386184266991634344483x8 + 1055793633392402952768x7 - 6769150214799915444440x6 - 1552196159553019851407x5 + 4355671676506075568364x4 + 921754431147330625307x3 - 1108584774969076393499x2 - 217498966742521653325x + 51140551819476687829 \( 37^{72} \) $C_{37}$ (as 37T1) n/a
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