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Results (displaying all 48 matches)

Label Polynomial Discriminant Galois group Class group
18.4.1104886300311045259363.1 x18 - 9x17 + 41x16 - 124x15 + 274x14 - 462x13 + 605x12 - 614x11 + 473x10 - 264x9 + 102x8 - 40x7 + 43x6 - 50x5 + 32x4 - 7x3 - 7x2 + 6x - 1 \( -\,23^{6}\cdot 97^{4}\cdot 84307 \) 18T764 Trivial (GRH)
18.0.1151509603184371131187.1 x18 - 7x17 + 24x16 - 52x15 + 83x14 - 124x13 + 216x12 - 391x11 + 612x10 - 809x9 + 967x8 - 1093x7 + 1119x6 - 964x5 + 683x4 - 417x3 + 228x2 - 98x + 23 \( -\,31^{8}\cdot 67^{5} \) 18T764 Trivial
18.4.1151509603184371131187.1 x18 - 2x17 - x16 + 3x15 + 13x14 - 22x13 - 28x12 + 63x11 + 27x10 - 98x9 - 22x8 + 99x7 + 28x6 - 60x5 - 26x4 + 17x3 + 9x2 - x - 1 \( -\,31^{8}\cdot 67^{5} \) 18T764 Trivial (GRH)
18.6.1905799670777912152064.1 x18 - 3x17 + 11x15 - 16x14 - 6x13 + 10x12 + 67x11 - 69x10 - 55x9 + 14x8 + 79x7 + 24x6 - 71x5 - 3x4 + 19x3 + 9x2 - 11x + 1 \( 2^{12}\cdot 19^{6}\cdot 31^{4}\cdot 10709 \) 18T764 Trivial (GRH)
18.0.3221287037577650765824.3 x18 + 2x16 - 5x14 - 11x12 - 2x10 + 11x8 + 21x6 + 18x4 + 7x2 + 1 \( -\,2^{18}\cdot 31^{6}\cdot 61^{4} \) 18T764 Trivial
18.2.4766811844970691743744.1 x18 - 9x17 + 35x16 - 76x15 + 99x14 - 77x13 + 33x12 - 3x11 - 12x10 + 16x9 - 3x8 - 13x7 + 9x6 + 9x5 - 11x4 - x3 + 3x2 - 1 \( 2^{12}\cdot 11^{6}\cdot 43^{4}\cdot 192149 \) 18T764 Trivial
18.2.5712191033975802990592.1 x18 - 9x17 + 44x16 - 148x15 + 379x14 - 777x13 + 1314x12 - 1865x11 + 2244x10 - 2299x9 + 2008x8 - 1493x7 + 940x6 - 495x5 + 211x4 - 68x3 + 14x2 - x - 1 \( 2^{12}\cdot 11^{6}\cdot 43^{4}\cdot 230257 \) 18T764 Trivial
18.8.18109005182056552997227.1 x18 - 4x17 - x16 + 20x15 - 21x14 - 22x13 + 73x12 - 38x11 - 94x10 + 88x9 + 26x8 - 48x7 + 42x6 - 7x5 - 33x4 + 13x3 + 8x2 - 3x - 1 \( -\,37^{4}\cdot 67\cdot 229^{6} \) 18T764 Trivial (GRH)
18.8.18109005182056552997227.2 x18 - 5x17 + 4x16 + 23x15 - 74x14 + 100x13 - 53x12 - 48x11 + 139x10 - 173x9 + 139x8 - 48x7 - 53x6 + 100x5 - 74x4 + 23x3 + 4x2 - 5x + 1 \( -\,37^{4}\cdot 67\cdot 229^{6} \) 18T764 Trivial (GRH)
18.6.27298649602801669443581.1 x18 - 4x17 + 5x16 - 2x15 - x14 + 6x13 - 12x12 + 15x11 - 18x10 + 21x9 - 18x8 + 15x7 - 12x6 + 6x5 - x4 - 2x3 + 5x2 - 4x + 1 \( 37^{4}\cdot 101\cdot 229^{6} \) 18T764 Trivial (GRH)
18.6.27298649602801669443581.2 x18 - x17 - 7x16 + 3x15 - 4x14 - 23x13 + 14x12 - 16x11 - 29x10 + 23x9 - 29x8 - 16x7 + 14x6 - 23x5 - 4x4 + 3x3 - 7x2 - x + 1 \( 37^{4}\cdot 101\cdot 229^{6} \) 18T764 Trivial
18.12.51624178951832860036871.1 x18 - 2x17 - 8x16 + 24x15 - 8x14 - 8x13 - 30x12 - 9x11 + 103x10 - 10x9 - 41x8 - 96x7 + 41x6 + 99x5 - 44x4 - 27x3 + 13x2 + 2x - 1 \( -\,37^{4}\cdot 191\cdot 229^{6} \) 18T764 Trivial (GRH)
18.8.51624178951832860036871.1 x18 - x17 - 9x16 + 12x15 + 18x14 - 58x13 + 15x12 + 122x11 - 38x10 - 31x9 + 54x8 - 37x7 - 15x6 + 9x5 + 2x4 + 8x3 + 7x2 + 4x + 1 \( -\,37^{4}\cdot 191\cdot 229^{6} \) 18T764 Trivial (GRH)
18.6.52868547747587848371273.1 x18 - 9x16 + 29x14 - 10x13 - 41x12 + 74x11 + 39x10 - 166x9 - 20x8 + 101x7 - 142x6 - 43x5 + 165x4 + 83x3 + 32x2 - 9x - 1 \( 3^{8}\cdot 127\cdot 211^{6}\cdot 719 \) 18T764 Trivial (GRH)
18.12.1107081869040352851890176.1 x18 - 10x16 + 26x14 + 29x12 - 188x10 + 125x8 + 158x6 - 81x4 + 3x2 + 1 \( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.4.1107081869040352851890176.1 x18 + 5x16 - 6x14 - 44x12 - 16x10 + 80x8 + 105x6 + 53x4 + 12x2 + 1 \( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.8.1107081869040352851890176.1 x18 - 4x16 - 9x14 + 28x12 + 44x10 - 33x8 - 70x6 - 26x4 + x2 + 1 \( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.12.1107081869040352851890176.2 x18 - 10x16 + 32x14 - 18x12 - 92x10 + 150x8 + 13x6 - 150x4 + 72x2 + 1 \( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.12.1107081869040352851890176.3 x18 - 6x16 + 4x14 + 43x12 - 114x10 + 96x8 - 6x6 - 22x4 + 4x2 + 1 \( -\,2^{12}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.10.16974084096094531116102281.1 x18 - 9x17 + 32x16 - 52x15 + 10x14 + 126x13 - 258x12 + 196x11 + 86x10 - 320x9 + 257x8 + 6x7 - 165x6 + 113x5 - 4x4 - 34x3 + 15x2 - 1 \( 37^{4}\cdot 229^{6}\cdot 62801 \) 18T764 Trivial (GRH)
18.10.23380151989531222748958669.1 x18 - 4x17 - 11x16 + 46x15 + 58x14 - 203x13 - 201x12 + 406x11 + 434x10 - 283x9 - 413x8 - 115x7 - 98x6 + 57x5 + 321x4 + 198x3 - 36x2 - 81x - 27 \( 3^{9}\cdot 7^{5}\cdot 643^{6} \) 18T764 Trivial (GRH)
18.4.40962029154493055519936512.1 x18 + 11x16 + 27x14 - 67x12 - 347x10 - 362x8 + 124x6 + 407x4 + 222x2 + 37 \( -\,2^{12}\cdot 37^{5}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.14.40962029154493055519936512.1 x18 - 3x17 - 7x16 + 41x15 - 41x14 - 183x13 + 425x12 + 180x11 - 989x10 + 557x9 + 389x8 - 1221x7 + 568x6 + 1110x5 - 312x4 - 475x3 - 95x2 + x + 1 \( 2^{12}\cdot 37^{5}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.14.40962029154493055519936512.2 x18 - 14x16 + 46x14 + 104x12 - 753x10 + 947x8 + 336x6 - 1221x4 + 592x2 - 37 \( 2^{12}\cdot 37^{5}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.16.70853239618582582520971264.1 x18 - 14x16 + 67x14 - 125x12 + 12x10 + 272x8 - 366x6 + 190x4 - 37x2 + 1 \( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.16.70853239618582582520971264.2 x18 - 9x16 + 21x14 + 25x12 - 182x10 + 303x8 - 229x6 + 85x4 - 15x2 + 1 \( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.4.70853239618582582520971264.3 x18 + 13x16 + 47x14 + 30x12 - 95x10 - 120x8 + 25x6 + 76x4 + 23x2 + 1 \( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \) 18T764 $[2]$ (GRH)
18.8.70853239618582582520971264.3 x18 - 16x14 - 15x12 + 68x10 + 120x8 + 12x6 - 70x4 - 28x2 + 1 \( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.4.70853239618582582520971264.4 x18 + 12x16 + 40x14 + 28x12 - 84x10 - 152x8 - 47x6 + 46x4 + 24x2 + 1 \( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \) 18T764 $[2]$ (GRH)
18.8.70853239618582582520971264.4 x18 + x16 - 16x14 - 9x12 + 70x10 + 3x8 - 73x6 - 4x4 + 18x2 + 1 \( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.6.1145627447487029914698974781.1 x18 - 2x17 + x16 - 24x15 + 73x14 - 32x13 + 103x12 - 124x11 + 67x10 - 591x9 + 286x8 + 925x7 - 869x6 + 44x5 + 120x4 - 51x3 + 18x2 + 7x - 1 \( 3^{9}\cdot 7^{7}\cdot 643^{6} \) 18T764 $[2]$ (GRH)
18.10.2621569865887555553275936768.1 x18 - 15x16 + 58x14 + 25x12 - 374x10 - 25x8 + 780x6 + 481x4 - 37x2 - 37 \( 2^{18}\cdot 37^{5}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.2.2621569865887555553275936768.1 x18 + 14x16 + 66x14 + 79x12 - 325x10 - 1301x8 - 1911x6 - 1332x4 - 407x2 - 37 \( 2^{18}\cdot 37^{5}\cdot 229^{6} \) 18T764 $[2]$ (GRH)
18.10.2621569865887555553275936768.2 x18 + 3x16 - 43x14 - 38x12 + 559x10 - 432x8 - 967x6 + 666x4 + 481x2 - 37 \( 2^{18}\cdot 37^{5}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.2.2621569865887555553275936768.2 x18 + 21x16 + 171x14 + 712x12 + 1643x10 + 2085x8 + 1300x6 + 222x4 - 111x2 - 37 \( 2^{18}\cdot 37^{5}\cdot 229^{6} \) 18T764 $[4]$ (GRH)
18.18.56014785910767366511898271121.1 x18 - 9x17 + 14x16 + 92x15 - 286x14 - 322x13 + 1786x12 + 308x11 - 5890x10 + 696x9 + 11753x8 - 1650x7 - 14569x6 + 177x5 + 10414x4 + 1966x3 - 3197x2 - 1284x - 53 \( 37^{4}\cdot 229^{6}\cdot 207244441 \) 18T764 Trivial (GRH)
18.10.56077017912500993006793084928.1 x18 - 6x17 + 3x16 + 17x15 - 48x14 + 389x13 - 1180x12 + 2440x11 - 3279x10 - 3727x9 + 23138x8 - 68029x7 + 164870x6 - 299424x5 + 437019x4 - 451323x3 + 235570x2 - 20917x - 15287 \( 2^{12}\cdot 37^{7}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.6.56077017912500993006793084928.1 x18 - x17 - 14x16 - 26x15 - 82x14 - 36x13 + 179x12 + 1110x11 + 3567x10 + 6413x9 + 10324x8 + 9116x7 + 10321x6 + 6455x5 + 12643x4 + 9576x3 + 10296x2 + 3006x + 241 \( 2^{12}\cdot 37^{7}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.10.56077017912500993006793084928.2 x18 - x17 - 16x16 + 35x15 + 5x14 - 203x13 + 655x12 - 765x11 + 598x10 + 1621x9 - 10878x8 + 19717x7 - 7900x6 - 20488x5 + 2160x4 + 1529x3 + 4373x2 - 1757x + 131 \( 2^{12}\cdot 37^{7}\cdot 229^{6} \) 18T764 Trivial (GRH)
18.14.203570754703289182817608794112.1 x18 + 5x16 - 71x14 + 146x12 + 312x10 - 1634x8 + 2490x6 - 1665x4 + 444x2 - 37 \( 2^{18}\cdot 11^{6}\cdot 37^{5}\cdot 43^{6} \) 18T764 Trivial (GRH)
18.14.203570754703289182817608794112.2 x18 - 23x16 + 158x14 - 281x12 - 551x10 + 1629x8 - 1035x6 - 37x4 + 185x2 - 37 \( 2^{18}\cdot 11^{6}\cdot 37^{5}\cdot 43^{6} \) 18T764 Trivial (GRH)
18.12.226998761597913809492704493568.1 x18 - 4x16 - 31x14 + 188x12 - 233x10 - 182x8 + 341x6 + 55x4 - 93x2 + 7 \( -\,2^{18}\cdot 3^{6}\cdot 7^{5}\cdot 643^{6} \) 18T764 Trivial (GRH)
18.12.226998761597913809492704493568.2 x18 + 3x16 - 50x14 + 42x12 + 220x10 - 361x8 + 58x6 + 141x4 - 68x2 + 7 \( -\,2^{18}\cdot 3^{6}\cdot 7^{5}\cdot 643^{6} \) 18T764 Trivial (GRH)
18.6.226998761597913809492704493568.1 x18 - 3x16 - 50x14 - 42x12 + 220x10 + 361x8 + 58x6 - 141x4 - 68x2 - 7 \( 2^{18}\cdot 3^{6}\cdot 7^{5}\cdot 643^{6} \) 18T764 Trivial (GRH)
18.6.226998761597913809492704493568.2 x18 + 4x16 - 31x14 - 188x12 - 233x10 + 182x8 + 341x6 - 55x4 - 93x2 - 7 \( 2^{18}\cdot 3^{6}\cdot 7^{5}\cdot 643^{6} \) 18T764 Trivial (GRH)
18.0.1588991331185396666448931454976.2 x18 + 32x16 + 397x14 + 2438x12 + 8021x10 + 14812x8 + 15332x6 + 8282x4 + 1855x2 + 49 \( -\,2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 643^{6} \) 18T764 $[2, 2, 68]$ (GRH)
18.0.1588991331185396666448931454976.3 x18 + 25x16 + 249x14 + 1281x12 + 3721x10 + 6276x8 + 6048x6 + 3108x4 + 721x2 + 49 \( -\,2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 643^{6} \) 18T764 $[2, 192]$ (GRH)
18.18.6128966563143672856303021326336.1 x18 - 31x16 + 378x14 - 2345x12 + 8061x10 - 15687x8 + 16956x6 - 9648x4 + 2511x2 - 189 \( 2^{18}\cdot 3^{9}\cdot 7^{5}\cdot 643^{6} \) 18T764 Trivial (GRH)


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