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Label Polynomial Discriminant Galois group Class group
17.1.133094720815439153.1 x17 - 2x16 + 7x15 - 12x14 + 22x13 - 34x12 + 46x11 - 61x10 + 65x9 - 65x8 + 53x7 - 36x6 + 20x5 - 5x4 - x3 + 4x2 - 2x + 1 \( 316968877\cdot 419898389 \) $S_{17}$ (as 17T10) Trivial
17.1.231494845017984433.1 x17 - x16 + 2x13 + x12 - 5x11 + x10 + 3x9 + 3x8 - x7 - 7x6 + 2x5 + 6x4 + x3 - 3x2 - 3x - 1 \( 59^{2}\cdot 1217\cdot 1579\cdot 34607051 \) $S_{17}$ (as 17T10) Trivial
17.3.1586349738982991023.1 x17 - x15 - x14 - 5x13 + 4x12 + x11 + 15x9 - 13x8 - 2x7 + 7x6 - 18x5 + 20x4 - 10x3 + 6x2 - 4x + 1 \( -\,2131\cdot 546781\cdot 1361451193 \) $S_{17}$ (as 17T10) Trivial
17.3.1912319465404851491.1 x17 - 3x16 + 4x15 - 3x14 + x13 + 4x12 - 8x11 + 9x10 - 2x9 - 9x8 + 12x7 - x6 - 4x5 + 2x4 - 3x3 + x2 - x - 1 \( -\,227\cdot 2411\cdot 3533\cdot 988994191 \) $S_{17}$ (as 17T10) Trivial
17.3.2151149236330118383.1 x17 - 2x15 - 4x14 + 4x13 + 7x12 - 3x11 - 3x10 - 3x9 + 5x8 - 5x7 - 4x6 + 14x5 - 2x4 - 7x3 + 2x + 1 \( -\,37^{5}\cdot 433\cdot 5531\cdot 12953 \) $S_{17}$ (as 17T10) Trivial
17.3.2311521177047925203.1 x17 - x16 + x15 - 3x14 + 4x13 - 4x12 - x11 + 4x10 - 5x9 + 17x8 - 42x7 + 59x6 - 45x5 + 9x4 + 15x3 - 15x2 + 6x - 1 \( -\,16843\cdot 137239279050521 \) $S_{17}$ (as 17T10) Trivial
17.3.2757250718309135423.1 x17 - 3x16 + 7x15 - 10x14 + 12x13 - 11x12 + 10x11 - 7x10 + 2x9 + 5x8 - 13x7 + 11x6 - 5x5 - 6x4 + 11x3 - 9x2 + 5x - 1 \( -\,75653\cdot 3119681\cdot 11682611 \) $S_{17}$ (as 17T10) Trivial
17.5.3621113810274499901.1 x17 - 5x15 - x14 + 5x13 + 6x12 + 9x11 - 16x10 - 21x9 + 19x8 + 13x7 - 5x6 - 4x5 - 5x4 + 3x3 - x + 1 \( 55954279\cdot 64715583419 \) $S_{17}$ (as 17T10) Trivial
17.3.3779800000525860359.1 x17 - 4x16 + 12x15 - 26x14 + 48x13 - 75x12 + 105x11 - 126x10 + 136x9 - 129x8 + 107x7 - 80x6 + 47x5 - 23x4 + 11x3 - 2x2 - 2x + 1 \( -\,137\cdot 1926157\cdot 14323744651 \) $S_{17}$ (as 17T10) Trivial
17.5.4755937542258621701.1 x17 - 6x15 - 2x14 + 17x13 + 13x12 - 27x11 - 34x10 + 20x9 + 47x8 - 38x6 - 13x5 + 17x4 + 12x3 - 2x2 - 3x - 1 \( 97\cdot 2927\cdot 2315407\cdot 7234597 \) $S_{17}$ (as 17T10) Trivial
17.5.14517428819890014793.1 x17 - 2x16 + 4x15 - 2x14 + 6x12 - 5x11 + x10 + 3x9 - 6x8 - 7x7 - x6 - 5x5 - 9x4 - 3x3 - 2x2 - 3x - 1 \( 10170343\cdot 1427427651151 \) $S_{17}$ (as 17T10) Trivial
17.5.89056089711131593861.1 x17 - 2x16 - 5x15 + 8x14 + 14x13 - 6x12 - 34x11 - 12x10 + 42x9 + 47x8 - 33x7 - 52x6 + 13x5 + 21x4 + 3x3 - 5x2 - 2x + 1 \( 946391\cdot 3063653\cdot 30715207 \) $S_{17}$ (as 17T10) Trivial
17.1.142063412679164600644.1 x17 - 2x16 - x15 + 5x14 - x13 - 8x12 + 6x11 + 8x10 - 11x9 - 3x8 + 13x7 - 3x6 - 8x5 + 5x4 + 3x3 - 3x2 + 1 \( 2^{2}\cdot 1697\cdot 20928611178427313 \) $S_{17}$ (as 17T10) Trivial
17.1.463009808974713123841.1 x17 - x16 - x15 - x14 + x12 + 13x11 + 7x10 + 11x9 + 4x8 + x7 + 7x6 + 23x5 + 31x4 + 42x3 + 24x2 + 6x - 1 \( 383^{8} \) $D_{17}$ (as 17T2) Trivial
17.1.808793517812627212561.1 x17 - x - 1 \( 808793517812627212561 \) $S_{17}$ (as 17T10) Trivial
17.1.1030463898345852385032.1 x17 - 2x16 - x15 + 5x14 - x13 - 8x12 + 6x11 + 8x10 - 11x9 - 3x8 + 12x7 - 3x6 - 7x5 + 5x4 + 3x3 - 3x2 + 1 \( 2^{3}\cdot 3^{2}\cdot 373\cdot 38369969405192597 \) $S_{17}$ (as 17T10) Trivial
17.3.2074524434943857177144.1 x17 - 2x16 + x15 + 2x14 - 3x13 + 3x11 - 3x10 - x9 + 6x8 - 5x7 - 4x6 + 8x5 - 3x4 - 4x3 + 3x2 - 1 \( -\,2^{3}\cdot 17\cdot 20759\cdot 9318913\cdot 78851137 \) $S_{17}$ (as 17T10) Trivial
17.3.8553979677514650635476.1 x17 - 3x16 + 4x15 + x14 - 13x13 + 26x12 - 25x11 + 2x10 + 35x9 - 62x8 + 59x7 - 25x6 - 13x5 + 33x4 - 30x3 + 17x2 - 6x + 1 \( -\,2^{2}\cdot 11\cdot 53\cdot 34759\cdot 105529138935877 \) $S_{17}$ (as 17T10) Trivial
17.1.17578609656292078845952.1 x17 - 4x - 4 \( 2^{16}\cdot 63535033\cdot 4221738529 \) $S_{17}$ (as 17T10) Trivial
17.1.124890250818288107857441.1 x17 - 4x16 + 6x15 - 5x14 + 7x13 - 17x12 + 24x11 - 16x10 + 42x9 - 83x8 + 82x7 - 72x6 + 37x5 + 24x4 - 10x3 + 14x2 - 2x + 1 \( 11^{8}\cdot 17^{12} \) $C_{17}:C_{4}$ (as 17T3) Trivial
17.1.239072435685151324847153.1 x17 - 34x12 + 17x11 + 85x10 + 102x9 - 170x8 - 272x7 - 68x6 + 255x5 + 255x4 + 68x3 + 17x2 + 17x + 4 \( 17^{19} \) $F_{17}$ (as 17T5) Trivial
17.1.604462909807314587353088.1 x17 - 2x16 + 8x13 + 16x12 - 16x11 + 64x9 - 32x8 - 80x7 + 32x6 + 40x5 + 80x4 + 16x3 - 128x2 - 2x + 68 \( 2^{79} \) $F_{17}$ (as 17T5) Trivial
17.1.930227631978098127294721.1 x17 - x16 + 4x15 - 18x14 + 11x13 + 14x12 + 21x11 - 62x10 + 14x9 + 50x8 + 54x7 - 121x6 - 7x5 + 36x4 + 64x3 - 23x2 + 43x + 1 \( 991^{8} \) $D_{17}$ (as 17T2) Trivial
17.1.1837263966425479287178561.1 x17 - x16 + 5x15 - 19x14 + 26x13 - 30x12 + 44x11 - 48x10 + 39x9 - 62x8 + 30x7 + 112x6 - 4x5 + 16x4 - 62x3 + 180x2 + 35x + 49 \( 13^{8}\cdot 83^{8} \) $D_{17}$ (as 17T2) Trivial
17.1.2007233999721653909999521.1 x17 - 2x16 + 4x15 - 18x14 + 10x13 - 16x12 + 44x11 + 10x10 + 72x9 + 18x8 + 134x7 + 88x6 + 275x5 + 200x4 + 220x3 + 240x2 + 80x + 64 \( 1091^{8} \) $D_{17}$ (as 17T2) Trivial (GRH)
17.1.2418678879491144686176529.1 x17 + 2x - 1 \( 71437\cdot 234281\cdot 144516666425357 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.6561080120160164763992064.1 x17 + 4x - 4 \( 2^{16}\cdot 3\cdot 33371379191895369283 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.10582983069512347410470401.1 x17 - 3x16 - 2x15 + 24x14 - 20x13 - 80x12 + 115x11 + 27x10 + 132x9 - 302x8 - 219x7 - 172x6 + 41x5 - 25x4 + 44x3 + 39x2 - 2x - 23 \( 17^{8}\cdot 79^{8} \) $D_{17}$ (as 17T2) Trivial
17.1.16071318903145633687890625.1 x17 - 4x16 + x15 + 16x14 - 30x13 - 2x12 + 88x11 + 143x10 + 133x9 - 515x8 - 803x7 - 68x6 + 1252x5 + 2972x4 + 2855x3 + 1505x2 + 550x + 125 \( 5^{8}\cdot 283^{8} \) $D_{17}$ (as 17T2) Trivial (GRH)
17.1.34895459505131153638432321.1 x17 - 2x16 - 3x14 + 24x13 + 18x12 - 138x10 - 203x9 - 75x8 + 352x7 + 588x6 + 384x5 + 132x4 + 493x3 + 1015x2 + 874x + 337 \( 1559^{8} \) $D_{17}$ (as 17T2) Trivial
17.1.37103038784156796454937761.1 x17 - x16 + 5x15 + 9x14 - 13x13 + 17x12 + 56x11 - 62x10 + 55x9 - 535x8 + 181x7 - 1027x6 + 661x5 - 1041x4 + 166x3 - 416x2 - 88x - 16 \( 1571^{8} \) $D_{17}$ (as 17T2) Trivial (GRH)
17.5.37475477362914554710500388.1 x17 - x16 - 4x15 + 4x14 + 6x13 - 6x12 - 8x11 + 8x10 + 9x9 - 7x8 - 9x7 + 3x6 + 9x5 - 2x4 - 6x3 + 4x2 + 2x - 1 \( 2^{2}\cdot 9368869340728638677625097 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.44542611246065932779454464.1 x17 - 4x9 - 18x6 - 12x3 + 4x - 2 \( 2^{16}\cdot 3\cdot 271\cdot 835997920414096373 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.5.47814524918055414168841988.1 x17 - 2x16 - 2x15 + 9x14 - 8x13 - 6x12 + 22x11 - 20x10 - 4x9 + 23x8 - 20x7 + 7x6 + x5 - 11x4 + 11x3 - x2 - 3x + 1 \( 2^{2}\cdot 71\cdot 113\cdot 398023\cdot 3743302227733793 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.51796166163753707827691520.1 x17 - 2x - 2 \( 2^{16}\cdot 3\cdot 5\cdot 379\cdot 139023179197698797 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.54213999356238892467552256.1 x17 - x - 2 \( 2^{16}\cdot 2387563\cdot 346478807223667 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.54214017802701491200393216.1 x17 - x - 4 \( 2^{16}\cdot 67\cdot 12346869580328982043 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.54214017802982966177103872.1 x17 - 2 \( 2^{16}\cdot 17^{17} \) $F_{17}$ (as 17T5) Trivial
17.1.56631869442212224526516224.1 x17 + 2x - 2 \( 2^{16}\cdot 23\cdot 37\cdot 67\cdot 15155721101316377 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.58497592625273225470725121.1 x17 - 2x16 + 9x15 - 23x14 + 59x13 - 112x12 + 156x11 - 49x10 + 221x9 - 25x8 - 162x7 - 4x6 + 553x5 + 1435x4 + 1716x3 + 1462x2 + 615x + 225 \( 1663^{8} \) $D_{17}$ (as 17T2) Trivial
17.1.63885424359899999574753280.1 x17 + 4x9 - 18x6 + 12x3 + 4x - 2 \( 2^{16}\cdot 5\cdot 7\cdot 27851834699314662203 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.92267897090016343666010049.1 x17 - 34x14 - 68x13 + 17x12 + 323x11 + 884x10 + 1241x9 + 1394x8 + 1003x7 + 935x6 + 663x5 + 901x4 + 578x3 + 493x2 + 136x + 57 \( 3^{8}\cdot 17^{18} \) $C_{17}:C_{8}$ (as 17T4) Trivial
17.1.102143502423134353014546241.1 x17 - 7x16 + 30x15 - 61x14 + 115x13 - 158x12 + 94x11 - 111x10 + 268x9 - 411x8 + 465x7 - 473x6 + 314x5 - 109x4 + 446x3 - 498x2 + 175x + 1 \( 1783^{8} \) $D_{17}$ (as 17T2) Trivial
17.1.133249137678121328919445504.1 x17 - 3x16 - 4x14 + 12x13 + 24x12 + 12x11 - 28x10 - 90x9 - 74x8 + 116x6 + 132x5 + 72x4 + 28x3 + 12x2 + 5x + 1 \( 2^{30}\cdot 137^{8} \) $\PSL(2,16)$ (as 17T6) $[15]$
17.1.323140727299350298506640625.1 x17 + 17x15 + 119x13 + 442x11 + 935x9 + 1122x7 + 714x5 + 204x3 + 17x - 1 \( 5^{8}\cdot 17^{17} \) $F_{17}$ (as 17T5) Trivial
17.1.861526607800060221948166144.1 x17 - x16 - 4x15 + 2x14 + 54x13 - 6x12 - 36x11 + 16x10 + 714x9 + 1238x8 + 484x7 - 764x6 - 1084x5 + 520x4 + 668x3 - 776x2 + 382x - 74 \( 2^{30}\cdot 173^{8} \) $\PSL(2,16)$ (as 17T6) $[15]$ (GRH)
17.1.1519687851595448316396690681.1 x17 + 3x - 3 \( 3^{16}\cdot 35388253\cdot 997597133837 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.13.2232673506822932495146063557.1 x17 - x16 - 17x15 + 17x14 + 112x13 - 115x12 - 356x11 + 389x10 + 547x9 - 675x8 - 342x7 + 560x6 + 27x5 - 205x4 + 42x3 + 24x2 - 10x + 1 \( 3^{3}\cdot 205542871\cdot 402308340646912121 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.3.2382214709257873624010389231.1 x17 - 3x - 1 \( -\,17987\cdot 132440913396223585034213 \) $S_{17}$ (as 17T10) Trivial (GRH)
17.1.2382216363738397396683917585.1 x17 + 3x - 1 \( 5\cdot 90341351171\cdot 5273811677288927 \) $S_{17}$ (as 17T10) Trivial (GRH)

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