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Results: (displaying matches 1-20 of 42)

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 \( -\,311^{9} \) $D_{19}$ 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 \( -\,359^{9} \) $D_{19}$ Trivial
19.1.75613185918270483380568064.1 x19 - 2x18 + 8x17 - 12x16 + 43x15 - 74x14 + 108x13 - 18x12 - 25x11 + 338x9 - 70x8 - 264x7 - 128x6 + 120x5 + 98x4 + 43x3 - 22x2 - 31x - 8 \( -\,2^{18}\cdot 19^{16} \) $F_{19}$ Trivial
19.3.146525077331272123613812972.1 x19 - 2x18 + 7x16 - 10x15 - x14 + 19x13 - 19x12 - 9x11 + 33x10 - 19x9 - 20x8 + 32x7 - 9x6 - 17x5 + 17x4 - 3x3 - 5x2 + 4x - 1 \( 2^{2}\cdot 139\cdot 126311\cdot 1021043\cdot 2043393285469 \) $S_{19}$ 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 \( -\,919^{9} \) $D_{19}$ Trivial
19.1.714209495693373205673756419.1 x19 + 19x15 - 19x14 - 19x13 + 171x12 + 19x11 - 266x10 + 19x9 + 475x8 + 741x7 + 437x6 + 38x5 - 38x4 - 19x3 + 1 \( -\,19^{21} \) $C_{19}:C_{6}$ Trivial
19.1.1733003264116942402576542823.1 x19 + 9x17 - 10x16 + 8x15 - 45x14 + 39x13 + 7x12 + 42x11 - 36x10 - 60x9 + 9x8 + 55x7 + 63x6 + 15x5 - 88x4 - 7x3 + 27x2 + 51x + 1 \( -\,1063^{9} \) $D_{19}$ 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 \( -\,11^{9}\cdot 109^{9} \) $D_{19}$ Trivial
19.3.7878347336355332175700013824.1 x19 - 2x18 + 7x16 - 10x15 - x14 + 19x13 - 19x12 - 9x11 + 33x10 - 19x9 - 20x8 + 33x7 - 9x6 - 18x5 + 17x4 - 3x3 - 5x2 + 4x - 1 \( 2^{8}\cdot 317\cdot 25373\cdot 137363\cdot 27854432176313 \) $S_{19}$ 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 \( -\,5^{9}\cdot 307^{9} \) $D_{19}$ 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 \( -\,1543^{9} \) $D_{19}$ 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 \( -\,3^{9}\cdot 557^{9} \) $D_{19}$ 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 \( 2^{2}\cdot 131\cdot 149\cdot 397\cdot 20117\cdot 218819\cdot 773146117559 \) $S_{19}$ 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 \( -\,2^{2}\cdot 49323595893763542101396994379 \) $S_{19}$ 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 \( -\,1831^{9} \) $D_{19}$ 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 \( -\,2^{7}\cdot 7\cdot 60259\cdot 4440286064038502416537 \) $S_{19}$ Trivial (GRH)
19.1.518630842213417245507316350976.1 x19 - 2 \( -\,2^{18}\cdot 19^{19} \) $F_{19}$ 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 \( -\,2^{2}\cdot 937\cdot 971\cdot 4676220259\cdot 93910895860973 \) $S_{19}$ Trivial (GRH)
19.1.3864100889961549978757771484375.1 x19 + 19x17 + 152x15 + 665x13 + 1729x11 + 2717x9 + 2508x7 + 1254x5 + 285x3 + 19x - 1 \( -\,5^{9}\cdot 19^{19} \) $F_{19}$ 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 \( 2^{10}\cdot 2746819\cdot 2958679616604904629509 \) $S_{19}$ Trivial (GRH)

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