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Label Polynomial Discriminant Galois group Class group
19.1.27217203547650508966391.1 x19 - x18 + 2x17 - 5x16 + 8x15 - 14x14 + 13x13 - 10x12 - x11 + 9x10 - 18x9 + 25x8 - 10x7 - 4x6 + 38x5 - 42x4 + 37x3 - 16x2 + 4x + 1 \( -\,311^{9} \) $D_{19}$ (as 19T2) Trivial
19.1.99048986760825351881639.1 x19 - 2x18 + 2x17 - 2x16 - 3x15 + 14x14 - 7x13 - 22x12 + 30x11 - 9x10 + 5x9 - 2x8 - 51x7 + 90x6 - 19x5 - 91x4 + 113x3 - 59x2 + 14x - 1 \( -\,359^{9} \) $D_{19}$ (as 19T2) Trivial
19.1.1939073247585017051548555.1 x19 - x - 1 \( -\,5\cdot 659\cdot 588489604729898953429 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.2017766063735610126699403.1 x19 + x - 1 \( -\,149\cdot 2063\cdot 6564253087266573169 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.75613185918270483380568064.1 x19 - 2x18 + 8x17 - 12x16 + 43x15 - 74x14 + 108x13 - 18x12 - 25x11 + 338x9 - 70x8 - 264x7 - 128x6 + 120x5 + 98x4 + 43x3 - 22x2 - 31x - 8 \( -\,2^{18}\cdot 19^{16} \) $F_{19}$ (as 19T6) Trivial
19.3.146525077331272123613812972.1 x19 - 2x18 + 7x16 - 10x15 - x14 + 19x13 - 19x12 - 9x11 + 33x10 - 19x9 - 20x8 + 32x7 - 9x6 - 17x5 + 17x4 - 3x3 - 5x2 + 4x - 1 \( 2^{2}\cdot 139\cdot 126311\cdot 1021043\cdot 2043393285469 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.467562425055097089773569879.1 x19 - 5x18 + 10x17 - 5x16 + 9x15 - 42x14 + 51x13 - 6x12 - 23x11 + 4x10 - 29x9 + 112x8 - 63x7 - 147x6 + 183x5 + 15x4 - 77x3 - 17x2 + 37x + 1 \( -\,919^{9} \) $D_{19}$ (as 19T2) Trivial
19.1.714209495693373205673756419.1 x19 + 19x15 - 19x14 - 19x13 + 171x12 + 19x11 - 266x10 + 19x9 + 475x8 + 741x7 + 437x6 + 38x5 - 38x4 - 19x3 + 1 \( -\,19^{21} \) $C_{19}:C_{6}$ (as 19T4) Trivial
19.1.1733003264116942402576542823.1 x19 + 9x17 - 10x16 + 8x15 - 45x14 + 39x13 + 7x12 + 42x11 - 36x10 - 60x9 + 9x8 + 55x7 + 63x6 + 15x5 - 88x4 - 7x3 + 27x2 + 51x + 1 \( -\,1063^{9} \) $D_{19}$ (as 19T2) Trivial
19.1.5121210743359411191500170799.1 x19 - 3x18 + 17x17 - 47x16 + 135x15 - 310x14 + 709x13 - 1319x12 + 2423x11 - 3757x10 + 5497x9 - 6561x8 + 7142x7 - 5699x6 + 4212x5 - 1490x4 + 482x3 + 408x2 - 210x + 49 \( -\,11^{9}\cdot 109^{9} \) $D_{19}$ (as 19T2) Trivial
19.3.7878347336355332175700013824.1 x19 - 2x18 + 7x16 - 10x15 - x14 + 19x13 - 19x12 - 9x11 + 33x10 - 19x9 - 20x8 + 33x7 - 9x6 - 18x5 + 17x4 - 3x3 - 5x2 + 4x - 1 \( 2^{8}\cdot 317\cdot 25373\cdot 137363\cdot 27854432176313 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.20630828016636731405933022091.1 x19 + 2x - 1 \( -\,7\cdot 233\cdot 12649189464522827348824661 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.22395541656295175507680165888.1 x19 + 4x - 4 \( -\,2^{18}\cdot 1699471\cdot 109607929\cdot 458633653 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.47312447868976594992787109375.1 x19 - 6x18 + 18x17 - 22x16 - 38x15 + 219x14 - 403x13 + 380x12 - 536x11 + 1378x10 - 1608x9 + 691x8 - 1073x7 + 1881x6 - 757x5 + 716x4 - 1464x3 + 513x2 - 10x + 295 \( -\,5^{9}\cdot 307^{9} \) $D_{19}$ (as 19T2) Trivial (GRH)
19.1.49578494467761916312526550343.1 x19 - 9x18 + 24x17 - 6x16 - 42x15 + 4x14 + 34x13 + 74x12 + 46x11 - 238x10 - 49x9 + 181x8 + 195x7 + 116x6 - 193x5 - 275x4 + 106x3 - 8x2 + 121x - 1 \( -\,1543^{9} \) $D_{19}$ (as 19T2) Trivial (GRH)
19.1.101575284882268140616515967431.1 x19 - 5x18 + 11x17 - 10x16 + 3x15 + 3x14 - 80x13 + 481x12 - 1180x11 + 1220x10 + 888x9 - 5070x8 + 8854x7 - 9440x6 + 6893x5 - 3748x4 + 2592x3 - 2790x2 + 2673x - 1053 \( -\,3^{9}\cdot 557^{9} \) $D_{19}$ (as 19T2) Trivial (GRH)
19.7.105491601716452677126377141804.1 x19 - 3x18 - x17 + 15x16 - 22x15 - 6x14 + 59x13 - 70x12 - 6x11 + 106x10 - 107x9 + 92x7 - 73x6 - x5 + 35x4 - 19x3 - x2 + 4x - 1 \( 2^{2}\cdot 131\cdot 149\cdot 397\cdot 20117\cdot 218819\cdot 773146117559 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.197294383575054168405587977516.1 x19 - 3x18 + 2x17 + 4x16 - 8x15 + 14x13 - 9x12 - 16x11 + 21x10 + 8x9 - 25x8 + 2x7 + 16x6 - 4x5 - 8x4 + 2x3 + 3x2 - x - 1 \( -\,2^{2}\cdot 49323595893763542101396994379 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.231310367559550740879663744871.1 x19 - 6x18 + 18x17 - 39x16 + 73x15 - 200x14 + 265x13 + 305x12 - 931x11 + 1905x10 - 5214x9 + 10284x8 - 13343x7 + 12719x6 - 8662x5 + 4443x4 - 1732x3 + 614x2 - 152x + 39 \( -\,1831^{9} \) $D_{19}$ (as 19T2) Trivial (GRH)
19.1.239740209347874920937820362368.1 x19 - 3x18 + 2x17 + 4x16 - 8x15 + 14x13 - 9x12 - 16x11 + 21x10 + 8x9 - 25x8 + 2x7 + 17x6 - 4x5 - 9x4 + 2x3 + 3x2 - x - 1 \( -\,2^{7}\cdot 7\cdot 60259\cdot 4440286064038502416537 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.436115443825492961137940758528.1 x19 - 8x - 8 \( -\,2^{18}\cdot 17\cdot 8627\cdot 11343650175290580793 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.477373143019455103322628554752.1 x19 - 4x - 4 \( -\,2^{18}\cdot 593\cdot 10949399\cdot 280461391706269 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.498001992616436174414972452864.1 x19 - 2x - 2 \( -\,2^{18}\cdot 11\cdot 29\cdot 8255287577\cdot 721386928637 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.518630802867009170210778775552.1 x19 - x - 2 \( -\,2^{19}\cdot 821\cdot 883013\cdot 15385297\cdot 88689509 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.518630842213267150872019351855.1 x19 - x - 4 \( -\,5\cdot 103726168442653430174403870371 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.518630842213417245507316350976.1 x19 - 2 \( -\,2^{18}\cdot 19^{19} \) $F_{19}$ (as 19T6) Trivial (GRH)
19.1.539259691810398316599660249088.1 x19 + 2x - 2 \( -\,2^{18}\cdot 7\cdot 47\cdot 1031\cdot 108139\cdot 56081694178207 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.601146240601341529876691943424.1 x19 + 8x - 8 \( -\,2^{18}\cdot 46553428447\cdot 49259334849493 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.9.1598194952468587114325789491156.1 x19 - 3x18 - 8x17 + 30x16 + 16x15 - 115x14 + 31x13 + 208x12 - 175x11 - 165x10 + 280x9 + 5x8 - 206x7 + 82x6 + 75x5 - 54x4 - 13x3 + 13x2 + x - 1 \( -\,2^{2}\cdot 937\cdot 971\cdot 4676220259\cdot 93910895860973 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.2074522739311139777284664197120.1 x19 - 4x - 8 \( -\,2^{20}\cdot 5\cdot 928238261\cdot 426273972622159 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.3864100889961549978757771484375.1 x19 + 19x17 + 152x15 + 665x13 + 1729x11 + 2717x9 + 2508x7 + 1254x5 + 285x3 + 19x - 1 \( -\,5^{9}\cdot 19^{19} \) $F_{19}$ (as 19T6) Trivial (GRH)
19.7.8322004363062341150231840635904.1 x19 - 3x18 - x17 + 15x16 - 22x15 - 6x14 + 59x13 - 70x12 - 6x11 + 106x10 - 107x9 - x8 + 92x7 - 72x6 - x5 + 35x4 - 19x3 - x2 + 4x - 1 \( 2^{10}\cdot 2746819\cdot 2958679616604904629509 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.5.8969938904536782790298366089328.1 x19 - 2x18 - 3x17 + 9x16 + x15 - 16x14 + 5x13 + 17x12 - 10x11 - 12x10 + 10x9 + x8 + 3x6 - 9x5 + 2x4 + 6x3 - 5x2 - x + 1 \( -\,2^{4}\cdot 3947\cdot 1431584761\cdot 99216821342546749 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.5.23920741637672928000872108534200.1 x19 - x18 - 6x17 + 7x16 + 13x15 - 21x14 - 16x13 + 41x12 + 10x11 - 51x10 + 5x9 + 43x8 - 19x7 - 24x6 + 18x5 + 5x4 - 11x3 + 2x2 + 3x - 1 \( -\,2^{3}\cdot 5^{2}\cdot 430709\cdot 19005923\cdot 14610723851226353 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.33192383974339170988381865771008.1 x19 + 4x - 8 \( -\,2^{24}\cdot 311\cdot 13913\cdot 49356007\cdot 9263974663 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.45730811992355144562119332263029.1 x19 - 3x - 1 \( 15451\cdot 1192721\cdot 1892107519\cdot 1311498030721 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.45730815949194455882746510510987.1 x19 + 3x - 1 \( -\,577\cdot 70079\cdot 1130954781811714100492789 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.46249444812988217467940237737984.1 x19 + 3x - 2 \( -\,2^{19}\cdot 613\cdot 7331\cdot 3070062337\cdot 6393898213 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.629287868530805907924458261644707.1 x19 - 9x - 9 \( -\,3^{18}\cdot 125471\cdot 142573\cdot 90800058249161 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.720749496472355508369324104418723.1 x19 - 3x - 3 \( -\,3^{18}\cdot 30011\cdot 461269\cdot 134390022739373 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.766459681593533327520664681907619.1 x19 - 2x - 3 \( -\,3^{18}\cdot 109\cdot 2111\cdot 2503\cdot 3435034858449743 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.766480310403783900516460488230307.1 x19 - x - 3 \( -\,3^{18}\cdot 733\cdot 5827\cdot 8053\cdot 2874523\cdot 20009947 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.766480310443130308591757025805731.1 x19 - 3 \( -\,3^{18}\cdot 19^{19} \) $F_{19}$ (as 19T6) Trivial (GRH)
19.1.766480310482476716667053563381155.1 x19 + x - 3 \( -\,3^{18}\cdot 5\cdot 11\cdot 277\cdot 1202769413\cdot 107967633989 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.13.801631882964189735135508990628664.1 x19 - 2x18 - 18x17 + 32x16 + 132x15 - 202x14 - 502x13 + 645x12 + 1045x11 - 1122x10 - 1176x9 + 1078x8 + 700x7 - 557x6 - 220x5 + 151x4 + 34x3 - 20x2 - 2x + 1 \( -\,2^{3}\cdot 13^{2}\cdot 17\cdot 3229\cdot 34365587\cdot 85132367\cdot 3692009831 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.812211124413905108814189947192739.1 x19 + 3x - 3 \( -\,3^{18}\cdot 581393\cdot 3605923841336588507 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.903672752355454709259055789966755.1 x19 + 9x - 9 \( -\,3^{18}\cdot 5\cdot 7\cdot 11\cdot 17\cdot 293990087\cdot 1212233453773 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.9.1388142379667992699741943954318476.1 x19 - 2x18 - 14x17 + 23x16 + 83x15 - 104x14 - 274x13 + 234x12 + 555x11 - 274x10 - 708x9 + 162x8 + 554x7 - 50x6 - 246x5 + 17x4 + 56x3 - 7x2 - 5x + 1 \( -\,2^{2}\cdot 347035594916998174935485988579619 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.1.1711431646479514505060267844358279.1 x19 + 7x - 4 \( -\,1711431646479514505060267844358279 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.13.6102326046691495371062145790782484.1 x19 - 3x18 - 12x17 + 40x16 + 52x15 - 216x14 - 88x13 + 614x12 + 8x11 - 987x10 + 143x9 + 904x8 - 163x7 - 461x6 + 72x5 + 128x4 - 14x3 - 18x2 + x + 1 \( -\,2^{2}\cdot 90313\cdot 16881409121807\cdot 1000636759045331 \) $S_{19}$ (as 19T8) Trivial (GRH)

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