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Label Polynomial Discriminant Galois group Class group
20.2.27487790694400000000000000.1 x20 - 2x19 + 11x18 - 24x17 + 65x16 - 152x15 + 296x14 - 552x13 + 819x12 - 1038x11 + 1045x10 - 784x9 + 371x8 + 32x7 - 244x6 + 272x5 - 185x4 + 90x3 - 39x2 + 8x - 1 \( -\,2^{52}\cdot 5^{14} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.0.76169967501312000000000000.1 x20 - 12x18 + 39x16 - 12x14 - 30x12 - 12x10 + 6x8 + 12x6 + 45x4 - 24x2 + 3 \( 2^{28}\cdot 3^{19}\cdot 5^{12} \) $D_4\times F_5$ (as 20T42) Trivial
20.0.87960930222080000000000000.1 x20 - 2x19 + 4x18 - 8x17 + 12x16 + 4x15 - 4x14 + 16x13 - 16x12 + 8x11 - 20x10 + 16x9 + 116x8 + 96x7 - 80x6 - 256x5 - 110x4 + 92x3 + 96x2 + 32x + 4 \( 2^{56}\cdot 5^{13} \) $D_4\times F_5$ (as 20T42) Trivial
20.2.109951162777600000000000000.1 x20 - 6x19 + 15x18 - 22x17 + 25x16 - 32x15 + 56x14 - 80x13 + 88x12 - 104x11 + 72x10 - 80x9 + 124x8 - 64x7 + 136x6 - 32x5 - 37x4 - 90x3 - 51x2 - 18x - 1 \( -\,2^{54}\cdot 5^{14} \) $D_4\times F_5$ (as 20T42) Trivial
20.0.2849723796343285750000000000.1 x20 + 7 \( 2^{10}\cdot 5^{12}\cdot 7^{19} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.0.66060088129912832000000000000.1 x20 + 14x10 + 32 \( 2^{27}\cdot 5^{12}\cdot 17^{10} \) $D_4\times F_5$ (as 20T42) Trivial
20.0.101559956668416000000000000000.1 x20 - x18 + 24x16 - 42x14 + 189x12 - 159x10 + 96x8 - 108x6 + 36x4 - 10x2 + 10 \( 2^{33}\cdot 3^{18}\cdot 5^{15} \) $D_4\times F_5$ (as 20T42) $[4]$ (GRH)
20.0.116226146700000000000000000000.1 x20 - 3x10 + 3 \( 2^{20}\cdot 3^{19}\cdot 5^{20} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.0.883304637884625106516765048832.1 x20 + x18 + x16 - 33x14 + 55x12 + 59x10 + 440x8 - 2112x6 + 512x4 + 4096x2 + 32768 \( 2^{27}\cdot 7^{10}\cdot 13^{12} \) $D_4\times F_5$ (as 20T42) $[3]$ (GRH)
20.10.1009491014725285836019160055808.1 x20 - 4x19 - 4x18 + 44x17 - 68x16 - 42x15 + 270x14 - 376x13 + 74x12 + 776x11 - 1639x10 + 908x9 + 1790x8 - 3164x7 + 1110x6 + 890x5 - 508x4 - 104x3 + 44x2 + 4x - 1 \( -\,2^{30}\cdot 7^{9}\cdot 13^{12} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.2.1083306204463104000000000000000.1 x20 + 10x18 - 20x17 + 32x16 - 100x15 + 110x14 + 80x13 - 156x12 + 400x11 - 1430x10 + 3000x9 - 3992x8 + 5360x7 - 7360x6 + 10400x5 - 11104x4 + 9600x3 - 5760x2 + 2560x - 640 \( -\,2^{38}\cdot 3^{17}\cdot 5^{15} \) $D_4\times F_5$ (as 20T42) $[2]$ (GRH)
20.0.1651502203247820800000000000000.1 x20 - 5x19 + 9x18 + 10x17 - 49x16 - 25x15 + 401x14 - 646x13 - 203x12 + 2129x11 - 2237x10 - 1404x9 + 7072x8 - 6760x7 + 1808x6 + 5360x5 - 1860x4 - 560x3 + 3946x2 - 274x + 1226 \( 2^{27}\cdot 5^{14}\cdot 17^{10} \) $D_4\times F_5$ (as 20T42) $[2]$ (GRH)
20.0.3615683187200000000000000000000.1 x20 - 10x10 + 32 \( 2^{27}\cdot 5^{20}\cdot 7^{10} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.4.4227845640314421248000000000000.1 x20 - 14x10 + 32 \( 2^{33}\cdot 5^{12}\cdot 17^{10} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.4.11863674982400000000000000000000.1 x20 - 14x15 - 435x10 + 958x5 + 1 \( 2^{30}\cdot 5^{20}\cdot 41^{5} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.2.54975581388800000000000000000000.1 x20 - 2 \( -\,2^{59}\cdot 5^{20} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.0.54975581388800000000000000000000.2 x20 + 2 \( 2^{59}\cdot 5^{20} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.10.73418021980786768815133779296875.1 x20 - 2x19 - 14x18 + 25x17 + 113x16 - 268x15 - 556x14 + 1786x13 + 1627x12 - 5838x11 - 3758x10 + 8861x9 + 7388x8 - 5488x7 - 6997x6 + 31x5 + 1642x4 + 269x3 - 7x2 - 9x - 1 \( -\,5^{10}\cdot 13^{12}\cdot 19^{9} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.2.121871948002099200000000000000000000.1 x20 - 3 \( -\,2^{40}\cdot 3^{19}\cdot 5^{20} \) $D_4\times F_5$ (as 20T42) $[2]$ (GRH)
20.20.1058528050256581320789626774678929408.1 x20 - 34x18 + 491x16 - 3920x14 + 18850x12 - 55698x10 + 98720x8 - 97708x6 + 47009x4 - 8664x2 + 112 \( 2^{50}\cdot 7^{9}\cdot 13^{12} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.0.1058528050256581320789626774678929408.1 x20 + 34x18 + 491x16 + 3920x14 + 18850x12 + 55698x10 + 98720x8 + 97708x6 + 47009x4 + 8664x2 + 112 \( 2^{50}\cdot 7^{9}\cdot 13^{12} \) $D_4\times F_5$ (as 20T42) $[2, 670]$ (GRH)
20.2.3059867626981844171358208000000000000.1 x20 - 7 \( -\,2^{40}\cdot 5^{12}\cdot 7^{19} \) $D_4\times F_5$ (as 20T42) $[2]$ (GRH)
20.0.15165274454805708800000000000000000000.1 x20 + 40x18 + 680x16 + 6400x14 + 36400x12 + 128048x10 + 272960x8 + 326720x6 + 179200x4 + 19200x2 + 128 \( 2^{49}\cdot 5^{20}\cdot 7^{10} \) $D_4\times F_5$ (as 20T42) $[2170]$ (GRH)
20.20.15165274454805708800000000000000000000.1 x20 - 40x18 + 680x16 - 6400x14 + 36400x12 - 128048x10 + 272960x8 - 326720x6 + 179200x4 - 19200x2 + 128 \( 2^{49}\cdot 5^{20}\cdot 7^{10} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.0.545211086046835507200000000000000000000.1 x20 - 10x19 + 45x18 - 120x17 + 220x16 - 284x15 + 130x14 + 640x13 - 2335x12 - 1890x11 + 29993x10 - 83440x9 + 127410x8 - 98360x7 + 89320x6 - 200888x5 + 312880x4 - 267040x3 + 191840x2 - 162240x + 71696 \( 2^{38}\cdot 3^{17}\cdot 5^{20}\cdot 11^{5} \) $D_4\times F_5$ (as 20T42) $[2]$ (GRH)
20.2.63895999874124585369600000000000000000000.1 x20 - 6 \( -\,2^{59}\cdot 3^{19}\cdot 5^{20} \) $D_4\times F_5$ (as 20T42) Trivial (GRH)
20.0.63895999874124585369600000000000000000000.1 x20 + 6 \( 2^{59}\cdot 3^{19}\cdot 5^{20} \) $D_4\times F_5$ (as 20T42) $[2]$ (GRH)
20.2.8231886620524584869068800000000000000000000.1 x20 + 53700x10 - 4608 \( -\,2^{33}\cdot 3^{18}\cdot 5^{20}\cdot 11^{10} \) $D_4\times F_5$ (as 20T42) $[2, 2]$ (GRH)
20.0.118905689229936268771490188271616000000000000000.1 x20 - 10x19 + 75x18 - 264x17 - 312x16 + 10716x15 - 19644x14 + 118446x13 + 1040871x12 - 2263018x11 + 2579485x10 + 65471640x9 + 46232796x8 - 146915028x7 - 380644878x6 + 280326630x5 + 1833189930x4 - 4763924676x3 + 6350854338x2 - 5069452068x + 1918665666 \( 2^{28}\cdot 3^{18}\cdot 5^{15}\cdot 7^{17}\cdot 11^{5} \) $D_4\times F_5$ (as 20T42) $[2, 20]$ (GRH)
20.0.1463762642505509948730468750000000000000000000000.1 x20 - 5x19 + 45x17 - 30x16 - 471x15 - 4620x14 + 10305x13 - 141585x12 + 606760x11 + 609838x10 - 1952580x9 + 28987335x8 - 74225835x7 + 179083080x6 - 244662507x5 + 710403480x4 - 436562865x3 - 5116531050x2 + 2621446065x + 6872217039 \( 2^{22}\cdot 3^{18}\cdot 5^{38}\cdot 19^{5} \) $D_4\times F_5$ (as 20T42) $[2]$ (GRH)
20.4.698172714027048240382400334267313536000000000000000.1 x20 + 65x18 - 2738x16 - 26292x15 - 218240x14 - 2265900x13 - 5195701x12 - 38299128x11 - 90961241x10 + 455452620x9 + 720754398x8 + 4471295556x7 + 25334742324x6 + 52611971412x5 - 122053122444x4 + 47805685956x3 + 795301311816x2 + 466959547656x - 2101842107004 \( 2^{22}\cdot 3^{17}\cdot 5^{15}\cdot 7^{18}\cdot 11^{10} \) $D_4\times F_5$ (as 20T42) $[2, 4, 20]$ (GRH)
20.0.158928787510637220000000000000000000000000000000000000.1 x20 - 10x19 + 105x18 - 660x17 + 3870x16 - 15852x15 + 59130x14 - 236400x13 + 877605x12 - 1837930x11 + 2750173x10 - 1729980x9 - 56073540x8 + 197617680x7 + 614328480x6 - 2562120432x5 + 2348943840x4 - 11563309440x3 + 25741488960x2 + 36027296640x + 11462824512 \( 2^{38}\cdot 3^{18}\cdot 5^{37}\cdot 29^{5} \) $D_4\times F_5$ (as 20T42) $[2, 20]$ (GRH)
20.2.15464197185473069561777343750000000000000000000000000000.1 x20 + 8362440x10 - 498225937500 \( -\,2^{28}\cdot 3^{17}\cdot 5^{37}\cdot 19^{10} \) $D_4\times F_5$ (as 20T42) $[2, 210]$ (GRH)
20.0.457263716717479671795708718299865722656250000000000000000.1 x20 - 5x19 + 20x18 + 35x17 - 110x16 - 14471x15 + 58720x14 - 37205x13 + 5614535x12 + 11523240x11 + 26044322x10 - 259765920x9 - 1244384545x8 - 14123682335x7 + 168604014460x6 - 439041788393x5 + 856847774500x4 - 248531078125x3 - 26823631243750x2 + 41896992259375x + 197430725614375 \( 2^{16}\cdot 3^{17}\cdot 5^{37}\cdot 11^{10}\cdot 31^{5} \) $D_4\times F_5$ (as 20T42) $[2, 2, 20]$ (GRH)
20.2.1024293792965275270740179588611492286838179568000000000000.1 x20 - 5x19 - 30x18 - 150x17 + 1365x16 + 6495x15 + 13290x14 - 163440x13 - 1387860x12 - 1430930x11 + 8552986x10 - 18873780x9 - 7336320x8 + 141614280x7 - 1202920740x6 - 4356308556x5 - 2480977080x4 - 24898685040x3 + 20689622640x2 + 83497187880x + 48728820456 \( -\,2^{16}\cdot 3^{18}\cdot 5^{12}\cdot 7^{17}\cdot 19^{10}\cdot 41^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.4.169781877136459328352384375000000000000000000000000000000000.1 x20 - 115x18 + 5770x16 - 1440x15 - 165830x14 - 82800x13 + 3014885x12 + 3272400x11 - 35378423x10 - 79322400x9 + 393756960x8 + 1323298800x7 + 4758606720x6 - 10520047440x5 + 55152558720x4 - 11607321600x3 + 171320650560x2 + 26672716800x - 189670693824 \( 2^{33}\cdot 3^{17}\cdot 5^{38}\cdot 29^{10} \) $D_4\times F_5$ (as 20T42) n/a
20.0.5395000787036562175590777878325808267813453824000000000000000.1 x20 - 120x18 + 7888x16 - 1764x15 - 45000x14 - 6315120x13 + 54010144x12 + 90853056x11 - 3602584704x10 + 14654077200x9 + 112702188032x8 - 1752566231808x7 + 11914781620224x6 - 54255565782264x5 + 184031339300816x4 - 477951506932032x3 + 893163408031104x2 - 1066289337176448x + 709016550047036 \( 2^{38}\cdot 3^{16}\cdot 5^{15}\cdot 7^{17}\cdot 11^{10}\cdot 19^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.2.18144464404222713605652682728648958381753368576000000000000000.1 x20 + 15x18 + 68x16 - 783210x14 + 11146009x12 + 1515223395x10 - 20127194318x8 + 88440811800x6 + 24804966751136x4 + 36520551394800x2 - 3143510018924000 \( -\,2^{33}\cdot 3^{16}\cdot 5^{15}\cdot 7^{18}\cdot 11^{5}\cdot 19^{10} \) $D_4\times F_5$ (as 20T42) n/a
20.0.398483907346819732159008478125000000000000000000000000000000000.1 x20 - 310x18 + 43720x16 - 2160x15 - 3692720x14 - 334800x13 + 206810960x12 + 85989600x11 - 8022023552x10 - 4850582400x9 + 219025145760x8 + 72940867200x7 - 3979561633920x6 + 1346584988160x5 + 55180067339520x4 - 43566888614400x3 - 351854399957760x2 + 249655655692800x + 1312243974648576 \( 2^{33}\cdot 3^{17}\cdot 5^{38}\cdot 11^{5}\cdot 19^{10} \) $D_4\times F_5$ (as 20T42) n/a
20.0.458049647307360970568988220106185818770836600455168000000000000.1 x20 - 115x18 + 23530x16 - 504x15 - 1799750x14 - 28980x13 + 192372005x12 + 117508860x11 - 10076499167x10 - 2189439000x9 + 701785854420x8 - 981609150060x7 - 23930956951560x6 + 15198620237892x5 + 1142620853270760x4 + 743631596719200x3 - 20343885662967660x2 - 4016545382792880x + 646041051363954996 \( 2^{28}\cdot 3^{17}\cdot 5^{12}\cdot 7^{18}\cdot 19^{5}\cdot 41^{10} \) $D_4\times F_5$ (as 20T42) n/a
20.2.497631011454939064202060220000000000000000000000000000000000000.1 x20 - 10x19 - 195x18 + 2040x17 + 14520x16 - 161532x15 - 492270x14 + 6684000x13 + 2200905x12 - 70749730x11 - 95388407x10 - 132271680x9 + 3154256910x8 + 22947160680x7 - 78897940920x6 - 233407352952x5 + 414207451440x4 + 410323462560x3 + 7262365534560x2 - 3991415434560x - 79045938974448 \( -\,2^{38}\cdot 3^{18}\cdot 5^{37}\cdot 11^{10}\cdot 19^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.0.608859383615347881779750989160156250000000000000000000000000000.1 x20 - 10x19 - 30x18 + 280x17 + 3960x16 - 18672x15 - 117440x14 + 213280x13 + 5426320x12 - 19560160x11 - 16160544x10 - 106188800x9 + 266531200x8 + 15243180800x7 - 50024230400x6 - 125420828160x5 + 636643200000x4 - 477334528000x3 + 410982528000x2 - 3924318464000x + 9480619878400 \( 2^{28}\cdot 3^{16}\cdot 5^{38}\cdot 11^{10}\cdot 89^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.2.779025894158619568967484436566138267517089843750000000000000000.1 x20 - 5x19 - 95x18 + 735x17 + 2585x16 - 33161x15 + 15315x14 + 1207235x13 - 10398055x12 + 20182195x11 - 30396651x10 + 607794475x9 + 1251634225x8 - 15837478375x7 + 56145238125x6 - 1676184575x5 + 718698621250x4 - 1527571833750x3 + 4635668881250x2 + 4515903081250x + 25851941971250 \( -\,2^{16}\cdot 3^{16}\cdot 5^{38}\cdot 29^{10}\cdot 71^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.0.4360353337131964370592434786665009884862483930746000000000000000.1 x20 - 5x19 - 99x18 + 258x17 + 49105x16 - 695863x15 + 8522143x14 - 8835250x13 + 1327351367x12 - 2196573753x11 + 173113722695x10 + 419389149256x9 + 12983556569844x8 + 15064947579416x7 + 705392864018584x6 + 713448227711744x5 + 14114690556587824x4 - 97626382174939856x3 + 95248235112201248x2 - 340409838530166384x + 12360603018214069136 \( 2^{16}\cdot 3^{17}\cdot 5^{15}\cdot 7^{18}\cdot 11^{17}\cdot 29^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.2.4994166215876227776290092298730468750000000000000000000000000000.1 x20 + 185x18 + 10170x16 - 15000x15 - 14430x14 + 1387500x13 - 14586315x12 - 840412500x11 - 9341523x10 - 24311775000x9 - 7942171740x8 - 2089986637500x7 - 2795604863880x6 - 43635003577500x5 + 87823626162120x4 - 573879860100000x3 + 1214937460911860x2 - 3858203116950000x + 4796675607065476 \( -\,2^{28}\cdot 3^{18}\cdot 5^{38}\cdot 11^{5}\cdot 31^{10} \) $D_4\times F_5$ (as 20T42) n/a
20.4.65971085909696290318640396673392028808593750000000000000000000000.1 x20 - 120x18 + 6035x16 - 480x15 - 164640x14 - 28800x13 + 2639530x12 - 357600x11 - 25260624x10 - 86400x9 + 157270150x8 + 289192800x7 + 20076000x6 - 4560186240x5 + 3385257125x4 + 18578652000x3 + 18457557000x2 + 27753840000x - 64435301225 \( 2^{22}\cdot 3^{16}\cdot 5^{37}\cdot 11^{5}\cdot 89^{10} \) $D_4\times F_5$ (as 20T42) n/a
20.0.56136275023201124305517265191938066406250000000000000000000000000000.1 x20 + 130x18 + 13285x16 - 5400x15 + 854360x14 + 351000x13 + 45780530x12 + 430677000x11 + 1809909476x10 + 9144603000x9 + 58085116650x8 - 1145774781000x7 + 2300599989000x6 - 21144057010200x5 + 15622931548125x4 + 235380065535000x3 + 690460909256250x2 + 1983734041725000x + 4004337882200625 \( 2^{28}\cdot 3^{16}\cdot 5^{37}\cdot 29^{5}\cdot 71^{10} \) $D_4\times F_5$ (as 20T42) n/a
20.0.252977010060091794322686019356947527998852560912646144000000000000000.1 x20 - 10x19 + 934x18 + 1812x17 + 343364x16 - 1970920x15 + 22330392x14 - 794403800x13 - 2922822172x12 - 108539004640x11 - 177532729296x10 + 10739485365224x9 + 148664630999080x8 + 1319017496324416x7 - 1573676037978240x6 - 143870078913265600x5 - 1007444850845660192x4 - 788955503763961632x3 + 33900336099376453616x2 + 356450589632390596448x + 1231798969663440772496 \( 2^{33}\cdot 3^{16}\cdot 5^{15}\cdot 7^{18}\cdot 11^{18}\cdot 19^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.0.84918716484613018665985720056760042383483090599116800000000000000000000.1 x20 + 730x18 + 238720x16 - 1512x15 + 46048400x14 + 551880x13 + 5802206480x12 + 260683920x11 + 498984475640x10 + 35717673600x9 + 29660149388520x8 + 2043573174720x7 + 1203701554412640x6 + 20051039556576x5 + 31870420079405760x4 - 2743310490056640x3 + 498948144686164800x2 - 86249720534725440x + 3491873768877677712 \( 2^{33}\cdot 3^{16}\cdot 5^{20}\cdot 7^{18}\cdot 31^{10}\cdot 71^{5} \) $D_4\times F_5$ (as 20T42) n/a
20.4.24464628993938796064014979732395474118735500796153036800000000000000000000.1 x20 - 720x18 - 4260x17 + 200975x16 + 2452248x15 - 18923040x14 - 508796400x13 - 1791460430x12 + 34935460920x11 + 429438591000x10 + 1258826067720x9 - 12907142561690x8 - 167452964989560x7 - 974654325915120x6 - 3541108213757136x5 - 8369601052982755x4 - 11880315149111640x3 - 6587629801123320x2 + 5606298645781020x + 7549200162029899 \( 2^{38}\cdot 3^{16}\cdot 5^{20}\cdot 7^{17}\cdot 31^{5}\cdot 71^{10} \) $D_4\times F_5$ (as 20T42) n/a
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